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comments elsewhere, I've become convinced that
Knowledge's coverage of quite a few (if not all) areas of maths require more top-down planning and structure: we have now too many gaps and overlaps as well as seriously uneven coverage due to (often very good) individual articles springing up on random topics based on authors' impulses to write them up. I've started to work on a plan on how the needed reorganisation could look like for algebraic topology (I thought about algebraic geometry first as a topic closer to my own turf but came to the conclusion that editorial complications there are harder and that topology should work as a test case). I've been planning to post a note to the
2102:. There's a new bonus prize of $ 200 worth of books of your choice to win for creating the most new women biographies between 0:00 on the 26th and 23:59 on 30th November. If you've been contributing to the contest, thank you for your support, we've produced over 2000 articles. If you haven't contributed yet, we would appreciate you taking the time to add entries to our articles achievements list by the end of the month. Thank you, and if participating, good luck with the finale!
281:(generated by open intervals) specified by the order structure, which one would assume to be a linearly ordered complete lattice (the latter being equivalent to the topological space being compact). Then lim inf and lim sup of a filter as well as of a function with values in such ordered topological space with respect to a filter would behave as expected. Whether it makes sense for some purposes to consider more general order structures I do not know.
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particularly meaningful. Also, for the set definition, the article suggests ambiguously that the ordering should be a complete lattice, which may be too restrictive as it still makes sense to talk about limits superior and inferior even in contexts where they are not guaranteed to exist. Do you know the most common definitions for these terms? If so, could you make sure the article matches them?
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concepts in the first sentence of the lead. However, I did now add "suitable" to qualify the subsets on which a measure is defined. While I'm afraid this is not going to help the reader too much, at least the next paragraph clarifies the situation and the meaning of "suitable". This way someone reading only the first paragraph is not left with a technically incorrect claim.
2064:. The idea is not to record every minor edit, but to create a momentum to motivate editors to produce good content improvements and creations and inspire people to work on more countries than they might otherwise work on. There's also the possibility of establishing smaller country or regional challenges for places like South East Asia, Japan/China or India etc, much like
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developing a comprehensive framework to discuss the various duals and dualities would be great, one could easily move into original research. This may make it necessary to make the article largely a summary, with wikilinks to individual dualities. I cannot think of many sources that would provide an overall framework covering all relevant dualities. Best,
2125:. Articles are typically reviewed for two weeks. If substantial concerns are not addressed during the review period, the article will be moved to the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Delist" in regards to the article's featured status. The instructions for the review process are
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2068:. For this to really work we need diversity and exciting content and editors from a broad range of countries regularly contributing. At some stage we hope to run some contests to benefit Asian content, a destubathon perhaps, aimed at reducing the stub count would be a good place to start, based on the current
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For the number of measures on the empty set, you are of course right. However, I feel the lead is not the best place to elaborate on (essentially trivial) technical exceptions such as this; I would not object to qualifying the "given set" by adding "non-empty", even though that comes in my mind close
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Hope this clarifies the picture. Hartshorne's
Residues and Duality and Grothendieck's Exposé I in SGA 5 are good sources for further information in the coherent and étale settings, while Iversen's book treats the topological (locally compact spaces) case and several texts (e.g., Mebkhout or Björk) on
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For the coherent duality the first statement says that the derived direct image commutes with the duality functors, and is simply an application of the adjunction property expressing the general duality result (first displayed formula above). Similarly, taking into account the biduality property, one
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I was reading your recent post at the talk page with interest. I had not realized that such a staple of dualities is lurking behind the harmless bidual of vector space... Just out of curiosity, one related question: the key point in
Poincaré or Verdier duality is, as far as I understand, not only the
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Hey Stca, I am writing you to let you know that the
Mathematics Collaboration of the week(soon to "of the month") is getting an overhaul of sorts and I would encourage you to participate in whatever way you can, i.e. nominate an article, contribute to an article, or sign up to be part of the project.
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for the limits superior and inferior of sets and filter bases look too general to me. In particular, they impose no conditions whatsoever on the relationship between the topology of the space involved and its partial ordering. Without some sort of order compatibility, the limits defined don't seem
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b) There is also the problem (which was there before you edited it) of the definition of a measure. In the first sentence of the lead, it is written that every subset has a measure. Without confusing the reader, there should be emphasis that the domain of the measure must be a sigma-algebra and not
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Thanks for the message; it's a pleasure to contribute, if only through comments this time - Groups will apparently be the first "real" mathematics article to get to FA (General relativity is more physics, and the rest either biographies or rather trivial maths). Comments just left on the FAC page.
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Hello, you seem like someone who's interested in sharing your knowledge. I see you have a PhD in alg. geom. and work in the financial sector. I may soon be completing mine, studying 4-manifolds. I had some questions about your vocational experiences. If you're curious or willing to talk to me could
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As for the definition for filters, first of all the most important definitions, those of lim inf and lim sup of a real-valued function with respect to a filter (base) are missing. And you're right, to have a meaningful theory one should link the topology and order structure together - a natural way
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In fact the whole article seems to be a bit of a mess. The section on sequences of real numbers contains way too much secondary trivia, lim inf and lim sup of real-valued functions is not even defined, the metric space (why metric?) definition does not impose any order structure on the codomain and
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The article is still quite seriously incomplete (I would classify it as Start class rather than B). In particular, relation between integral and measure should be developed. In addition a host of topics is still missing: discussion of
Lebesgue-measurable sets (and non-measurable ones!), measurable
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Thanks for kind words and the encouragement to push the article towards FA. I agree with the page number point for FA articles, and will put those in order. As for Google Books, I think that's an excellent advice. Indeed, that's the source I used to locate a few of the references in books read but
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First of all, congratulations on your GA on this article. This is a very nice piece of work, that should easily go through FAC. However, as it was pointed at GA/R, you will definitely need the page numbers for that. If you do have the book but don't have time to find the exact place, you might try
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which has produced near 200 articles in just three days. If you would like to see this happening for Asia, and see potential in this attracting more interest and editors for the country/countries you work on please sign up and being contributing to the challenge! This is a way we can target every
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functions, products of measures, outer measure, signed measures and Hahn decomposition, complex and more general vectorial measures, absolute value of a complex measure, key properties of bounded measures (including the norm), vague and other topologies on spaces of measures, support of a measure.
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As for the issue with "each" in the first sentence, you're obviously right again. I left it there after considering the options — given that the true state of affairs is revealed in the following paragraph, I preferred slight sloppiness to a convoluted sentence structure or introducing too many
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a) It is written, "there are in general infinitely many different measures on a given set, each assigning different "sizes" for subsets". This seems incorrect because the empty set has only one measure on its power set (the measure of the empty set must be either 0 or infinity, depending on the
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Given that there has apparently been quite some heated argumentation on the talk page, and given the amount of work the page would need, I'm somewhat hesitant to jump into editing it. I could do some expansion and fixing around filters, though (seems that by staying way from the usual undergrad
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Hello, and thanks for the compliments. I do quite enjoy it here, yes. Let's see, however, for how much longer I manage to have this luxury of some spare time to devote to
Knowledge. In any case, plans for what to do here keep accumulating like unread novels at my bedside... As you've seen in my
2031:
Thanks for the invitation to work on
Duality, this is a worthwhile and interesting initiative. However, I'm afraid the time I can give this work short term is extremely limited, perhaps some random hours in the weekends. I'll see what I can do. Initial thought about the article is that while
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mathematicians, which is something I don't know. The same goes for what sort of order is required. Requiring the order topology certainly works, but it's conceivable that a weaker condition would suffice to give interesting results. One possibility might be requiring that for each subset
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I completely forgot to watch for a response here. I'm sorry about that. I'm not yet convinced that the space should be required to be a complete lattice, although requiring it to be bounded-complete is likely sensible. Of course, the big question is how this actually is defined by working
229:, which made it appear that the current palace dates from the Heian period. It seems that some topics are sufficiently esoteric that it is at the same time possible and necessary to work on your own on them — the same appears to be happening with some more technical maths articles like
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And thanks for the message. I'll reply briefly here to avoid having to copy your comments to the article talk page (to simplify, perhaps you could leave the comments on article talk page, and just leave a notification to user talk page to alert an
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on the cross product. I was about to make precisely the same point, but wouldn't have done it nearly as well as you did: your comment about the product of real numbers being a pseudoreal was particularly nice! I hope you continue to enjoy it here.
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Not exactly my expertise (the modular form side of things is not one of my strengths...), but I'll see what I can do. Maybe start adding the structure to the description of the proof. However, this will not likely happen over the next few days.
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Hi, Fg2, and thanks for the kind remarks! This one started in May with the modest intention of creating a stub for the old palace, but grew quite quickly... The motivation was first just to correct a few statements made in the article on
237:, it certainly would be much worse without the comments received in Peer Review, the GA process and now in FA process. Despite some moderately excessive requests at times, the Knowledge collaboration model appears to work nicely.
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Thanks for confidence. I've unfortunately been too busy at work to respond earlier. The article appears to be very comprehensive - I just left a few minor comments on tensor products on the talk page. Great work!
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Hi, I'm trying to gather some people working on duality article. Are you up to it? I'd like to develop the article to Good
Article standard, but I think this is a broad topic so more hands/eyes would be good.
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The dualising functors and complexes and the various duality theorems are related in a number of ways, both in this coherent sheaf set-up and in the other contexts mentioned above. First, the functor
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On the other hand, your lead is far better than the initial one because it gives the applications of measure theory to probability. P.S Could you please respond on the talk page of the article? --
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conventions used). Maybe, there should be a discussion on the distinction between a "measure" and a "set function". I know you have noted this later on, but maybe it should be emphasized.
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526:, but people are busy/dizzy with LateX formatting and icon questions ;) But I remember your thorough review of the group article, so if you have a moment, could you review vector spaces?
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792:{\displaystyle \mathbf {R} f_{*}\mathbf {R} {\mathcal {H}}om({\mathcal {F}},f^{!}{\mathcal {G}})\cong \mathbf {R} {\mathcal {H}}om(\mathbf {R} f_{*}{\mathcal {F}},{\mathcal {G}}).}
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page and update the list with the taskforces in which you wish to participate. Links to all the taskforces are found at the top of the list of participants.
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In order to encourage more participation, and to help people find a specific area in which they are more able to help out, we have organized taskforces at
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country of Asia, and steadily vastly improve the encyclopedia. We need numbers to make this work so consider signing up as a participant! Thank you. --
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And you're right, the article on coherent duality needs work. As do the ones on
Verdier duality, and Poincaré duality and most other duality theorems.
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page with link to the outline once I get it done. If you wish, feel free to have a look at a work in progress and comment — the page is
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and am glad that someone has taken the time to improve the article! But I just wanted to confirm some dubious points in the lead:
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1094:{\displaystyle \mathbf {R} Hom({\mathcal {F}},\omega _{X/Y})\cong \mathbf {R} Hom(\mathbf {R} \Gamma (X,{\mathcal {F}}),k)}
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to
Featured Article status. It's remarkable that the article is so purely the work of one person. Again, congratulations!
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is talked about in page 713. I hope this can help you in building other great articles on very interesting subjects.
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is isomorphism. Notice that the simple algebraic biduality of vector spaces becomes the statement that on Spec(
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is a dualising complex if (i) it is quasi-isomorphic to a bounded complex of injective sheaves, and (ii) the
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Hi - I posted the section with the same name on my talk page. Could you take part in discussion ? Thanks ARP
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is indeed intriguing, and would (should we get there) be the first maths GA/FA article appealing to experts.
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takes dualising complexes to dualising complexes. Next, the dualising functors switch between the functors
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Thanks muchly. I think it might be good to more or less copy this to one of the said articles. Also,
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neccesarily be equal to the power set in question (or a sigma-ring depending on convention).
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Is there a similar sheafish/category-minded characterisation of reflexive top.v.sp.?
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can be more complicated. To recover the ordinary Serre duality for smooth projective
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Knowledge's Expert Peer Review process (or lack of such) for Science related articles
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1390:{\displaystyle D_{\mathcal {K}}=\mathbf {R} {\mathcal {H}}om(\cdot ,{\mathcal {K}})}
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625:-modules, however). For the coherent duality, one usually deals with the case where
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Talk:Mathematics#Making mathematics articles more accessible to a general readership
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Please let me know if you have any questions, and thank you for helping out! ···
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in duality, so perhaps we can write something together. Currently I'm on
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of relative differentials, shifted n spaces to the left. More generally
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that I'm editing at the moment. But while edits may be mostly mine in
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I thought say hello, and thank you for your interesting comments at
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satisfies the following biduality: the natural map of functors
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The discussion, to which you contributed, has been archived,
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you send me an email - jwilliam at math . utexas . edu?
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1707:
1706:
1680:
1678:
1677:
1672:
1670:
1669:
1657:
1656:
1647:
1639:
1638:
1629:
1621:
1620:
1581:
1579:
1578:
1573:
1571:
1570:
1564:
1563:
1551:
1550:
1533:
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1525:
1523:
1522:
1461:
1459:
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1451:
1450:
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1436:
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1434:
1421:
1396:
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1388:
1383:
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1361:
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1354:
1346:
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1319:
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1316:
1311:
1299:
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1239:
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1231:
1214:
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1198:
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1179:
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1134:
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1100:
1098:
1097:
1092:
1078:
1077:
1059:
1042:
1022:
1021:
1017:
1001:
1000:
982:
962:. Then applying
912:
910:
909:
904:
899:
898:
892:
891:
882:
880:
872:
861:
860:
856:
840:
839:
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772:
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764:
755:
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740:
734:
723:
722:
716:
715:
703:
702:
687:
686:
680:
675:
674:
665:
584:Coherent duality
530:. Thanks a lot.
528:This is the page
463:Talk:Mathematics
355:
353:
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198:
17:Mathematics CotW
2229:
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2199:
2146:
2111:
2096:
2085:
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2013:Jakob.scholbach
2008:
1951:
1946:
1924:
1906:Jakob.scholbach
1831:
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1335:
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1322:duality functor
1279:
1278:
1255:
1254:
1183:
1170:
1148:
1125:
1114:
1113:
1005:
973:
972:
929:
923:
883:
844:
824:
819:
818:
756:
707:
666:
656:
655:
648:
638:
620:
588:Jakob.scholbach
577:
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532:Jakob.scholbach
517:
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407:Jakob.scholbach
396:
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322:
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231:Fibred category
208:
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34:
19:
12:
11:
5:
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1615:
1596:
1589:
1569:
1562:
1558:
1554:
1549:
1521:
1507:
1497:
1475:is dualising.
1465:
1464:
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1462:
1448:
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1428:
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1196:
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1186:
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1177:
1173:
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1166:
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1147:
1142:
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1132:
1128:
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1103:
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1090:
1087:
1084:
1081:
1076:
1071:
1068:
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1062:
1058:
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1045:
1041:
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1034:
1031:
1028:
1025:
1020:
1016:
1012:
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1004:
999:
994:
991:
988:
985:
981:
925:
919:
916:
915:
914:
913:
902:
897:
890:
886:
879:
875:
870:
867:
864:
859:
855:
851:
847:
843:
838:
831:
827:
802:
801:
800:
799:
788:
785:
780:
775:
770:
763:
759:
754:
750:
747:
744:
739:
733:
729:
726:
721:
714:
710:
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701:
696:
693:
690:
685:
679:
673:
669:
664:
646:
636:
618:
601:
600:
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575:
571:
564:
563:
547:
546:
516:
511:
495:
492:
478:
472:
466:
460:
454:
452:
446:
443:with very much
438:
435:
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392:
375:
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343:
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332:
329:
309:
282:
279:order topology
274:
249:
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207:
204:
180:
177:
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174:
173:
161:
160:
159:
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125:
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119:
118:
106:
105:
85:A-Class review
76:
73:
72:
71:
33:
30:
18:
15:
13:
10:
9:
6:
4:
3:
2:
2226:
2217:
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2208:
2207:Shhhnotsoloud
2204:
2196:
2190:
2186:
2182:
2178:
2174:
2170:
2166:
2165:
2162:
2159:
2154:
2149:
2143:
2141:
2140:
2136:
2132:
2131:Bumbubookworm
2128:
2124:
2120:
2116:
2108:
2105:
2103:
2101:
2094:
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2067:
2063:
2059:
2055:
2047:
2043:
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2030:
2029:
2025:
2024:
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2022:
2018:
2014:
2006:
2003:
1999:
1995:
1991:
1987:
1986:
1981:
1980:
1975:
1971:
1970:
1965:
1964:
1960:
1959:
1958:
1957:
1954:
1949:
1942:
1938:
1934:
1932:
1927:
1922:
1919:
1915:
1911:
1907:
1903:
1900:
1899:duality topic
1896:
1892:
1889:
1888:PaulTanenbaum
1885:
1881:
1880:
1879:
1878:
1874:
1870:
1865:
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1841:
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1747:
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1708:
1703:
1699:
1691:
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1687:
1666:
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1653:
1649:
1640:
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1622:
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1605:
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1602:
1601:
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1560:
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1503:
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1470:
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1426:
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1403:
1374:
1371:
1365:
1362:
1347:
1336:
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1327:
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1324:
1323:
1304:
1296:
1291:
1252:
1248:
1227:
1221:
1218:
1205:
1202:
1194:
1191:
1188:
1184:
1175:
1171:
1167:
1164:
1161:
1153:
1149:
1145:
1130:
1126:
1122:
1119:
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1111:
1110:
1109:
1108:
1085:
1082:
1069:
1066:
1049:
1046:
1043:
1035:
1026:
1018:
1014:
1010:
1006:
1002:
989:
986:
983:
971:
970:
969:
968:
967:
965:
961:
957:
953:
949:
945:
941:
938:over a field
937:
933:
928:
922:
900:
888:
884:
873:
865:
857:
853:
849:
845:
841:
829:
825:
817:
816:
815:
814:
813:
811:
807:
786:
773:
761:
757:
745:
742:
727:
712:
708:
704:
691:
688:
671:
667:
654:
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652:
651:
650:
645:
642:
635:
632:
628:
624:
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614:
610:
606:
597:
593:
589:
585:
581:
568:
567:
566:
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562:
558:
554:
549:
548:
544:
543:
542:
541:
537:
533:
529:
525:
520:
515:
514:Vector spaces
512:
510:
509:
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501:
491:
490:
486:
482:
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464:
458:
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155:
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147:
144:Sincerely, --
142:
140:
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123:
117:
114:
110:
109:
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107:
104:
101:
96:
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59:
54:
53:
52:
51:
48:
43:
39:
31:
29:
28:
25:
16:
2200:
2169:Heian Palace
2160:
2115:Heian Palace
2112:
2107:Heian Palace
2097:
2081:
2051:
2009:
1943:
1939:
1935:
1928:
1925:
1866:
1861:
1858:
1772:
1769:
1685:
1594:
1587:
1586:. Denote by
1583:
1535:
1504:
1501:
1494:
1491:
1490:and between
1487:
1483:
1479:
1477:
1472:
1468:
1466:
1401:
1321:
1250:
1246:
1244:
1106:
963:
959:
955:
951:
947:
943:
939:
935:
931:
926:
920:
917:
809:
805:
803:
643:
640:
633:
630:
626:
622:
615:
612:
608:
604:
602:
579:
521:
518:
497:
442:
440:
403:FAC comments
400:
397:
377:
278:
251:
235:Heian Palace
212:Heian Palace
209:
206:Heian Palace
193:
189:Participants
182:
157:not at hand.
143:
138:
135:this example
131:Google Books
127:
124:Heian Palace
113:Geometry guy
89:Geometry guy
78:
47:Geometry guy
35:
20:
524:round table
381:Orthografer
227:Kyoto Gosho
24:Cronholm144
1926:Hi Stca4!
481:Wavelength
394:groups FAC
146:SidiLemine
2201:I closed
2026:Hi Jakob,
1967:editor?).
950:) and on
545:Hi Jakob,
519:Hi Stca,
166:Regards,
2185:contribs
2144:Congrats
2052:Hi. The
1895:matrices
812:, then
574:f = (R)f
500:Apovolot
133:, as in
129:through
946:= Spek(
918:where ω
139:buraken
2117:for a
2034:Stca74
1990:Stca74
1884:Arcfrk
1869:Stca74
553:Stca74
423:Stca74
358:Dfeuer
287:Stca74
259:Dfeuer
239:Stca74
168:Stca74
100:Stca74
66:Stca74
38:WT:WPM
1249:: if
398:Hi,
32:Hello
2211:talk
2181:talk
2135:talk
2127:here
2060:and
2038:talk
2017:talk
1994:talk
1988:Br,
1910:talk
1886:and
1873:talk
1686:and
1593:and
1538:and
1500:and
1486:and
592:talk
557:talk
536:talk
504:talk
485:talk
471:and
459:and
427:talk
411:talk
385:talk
362:talk
291:talk
263:talk
62:here
2109:FAR
1961:Hi,
927:X/Y
921:X/Y
804:If
479:--
447:at
328:sup
216:Fg2
197:日本穣
75:FLT
2213:)
2187:)
2183:/
2137:)
2129:.
2040:)
2019:)
1996:)
1947:PS
1912:)
1875:)
1829:∘
1824:∗
1811:∘
1775::
1748:∗
1735:∘
1722:≅
1709:∘
1659:∘
1654:∗
1641:≅
1623:∘
1438:∘
1423:→
1372:⋅
1192:−
1162:≅
1150:ω
1061:Γ
1036:≅
1007:ω
889:∗
874:⊗
846:ω
762:∗
728:≅
672:∗
639:=
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334:∈
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.