577:
A space is locally
Hausdorff exactly if it can be written as a union of Hausdorff open subspaces. And in a locally Hausdorff space each point belongs to some Hausdorff dense open subspace.
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There are locally
Hausdorff spaces where a sequence has more than one limit. This can never happen for a Hausdorff space.
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587:. The converse is not true in general. For example, an infinite set with the
830:, Lecture Notes in Math., vol. 1488, Springer, Berlin, pp. 298–305,
874:
826:
Niefield, Susan B. (1991), "Weak products over a locally
Hausdorff locale",
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is locally
Hausdorff at every point, and is therefore
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and therefore the space is not locally
Hausdorff at
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682:is Hausdorff. This follows from the fact that if
895:Proceedings of the American Mathematical Society
863:Cahiers de topologie et géométrie différentielle
317:is not Hausdorff, but it is locally Hausdorff.
891:"Manifolds: Hausdorffness versus homogeneity"
8:
889:Baillif, Mathieu; Gabard, Alexandre (2008).
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859:"A note on the locally Hausdorff property"
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633:that is locally Hausdorff at some point
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298:is locally Hausdorff (it is in fact
809:topological groups are Hausdorff).
279:Examples and sufficient conditions
25:
602:Every locally Hausdorff space is
580:Every locally Hausdorff space is
526:any neighbourhood of it contains
313:of differentiable functions on a
480:is a Hausdorff neighbourhood of
599:that is not locally Hausdorff.
1:
918:10.1090/S0002-9939-07-09100-9
828:Category theory (Como, 1990)
980:
342:particular point topology
232:
857:Niefield, S. B. (1983).
387:is locally Hausdorff at
704:{\displaystyle y\in G,}
655:{\displaystyle x\in G,}
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344:with particular point
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135:(completely Hausdorff)
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473:{\displaystyle \{p\}}
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315:differential manifold
296:line with two origins
288:is locally Hausdorff.
263:if every point has a
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503:For any other point
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302:) but not Hausdorff.
735:to itself carrying
340:be a set given the
153:(regular Hausdorff)
947:, Proposition 3.5.
935:, Proposition 3.4.
836:10.1007/BFb0084228
788:
771:{\displaystyle y,}
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562:{\displaystyle x.}
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519:{\displaystyle x,}
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496:{\displaystyle p.}
493:
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454:and the singleton
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403:{\displaystyle p,}
400:
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360:{\displaystyle p.}
357:
330:
300:locally metrizable
251:, in the field of
206:(completely normal
188:(normal Hausdorff)
36:topological spaces
964:Separation axioms
791:{\displaystyle G}
748:{\displaystyle x}
728:{\displaystyle G}
675:{\displaystyle G}
631:topological group
622:{\displaystyle G}
589:cofinite topology
539:{\displaystyle p}
447:{\displaystyle X}
423:{\displaystyle p}
380:{\displaystyle X}
333:{\displaystyle X}
273:subspace topology
261:locally Hausdorff
257:topological space
245:
244:
226:(perfectly normal
31:Separation axioms
18:Locally Hausdorff
16:(Redirected from
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901:(3): 1105–1111.
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228: Hausdorff)
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711:there exists a
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286:Hausdorff space
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269:Hausdorff space
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432:isolated point
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259:is said to be
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45:classification
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945:Niefield 1983
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933:Niefield 1983
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713:homeomorphism
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265:neighbourhood
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908:math/0609098
898:
894:
884:
869:(1): 87–95.
866:
862:
852:
827:
821:
608:
601:
579:
576:
260:
246:
123:completely T
63:(Kolmogorov)
923:, Lemma 4.2
879:, Lemma 3.2
307:etale space
249:mathematics
170:(Tychonoff)
99:(Hausdorff)
813:References
573:Properties
367:The space
271:under the
267:that is a
43:Kolmogorov
875:2681-2398
693:∈
644:∈
117:(Urysohn)
81:(Fréchet)
958:Category
309:for the
253:topology
844:1173020
237:History
163:3½
873:
842:
805:(and T
430:is an
410:since
284:Every
222:
202:
184:
149:
131:
110:½
95:
77:
59:
903:arXiv
715:from
662:then
629:is a
604:sober
597:space
591:is a
311:sheaf
871:ISSN
320:Let
305:The
294:The
255:, a
913:doi
899:136
832:doi
778:so
755:to
609:If
434:in
247:In
34:in
960::
911:.
897:.
893:.
867:24
865:.
861:.
840:MR
838:,
606:.
275:.
921:.
915::
905::
877:.
847:.
834::
807:1
802:1
800:T
786:G
766:,
763:y
743:x
723:G
699:,
696:G
690:y
670:G
650:,
647:G
641:x
617:G
595:1
593:T
584:1
582:T
557:.
554:x
534:p
514:,
511:x
491:.
488:p
468:}
465:p
462:{
442:X
418:p
398:,
395:p
375:X
355:.
352:p
328:X
217:6
214:T
197:5
194:T
179:4
176:T
159:T
144:3
141:T
126:2
108:2
105:T
90:2
87:T
72:1
69:T
54:0
51:T
20:)
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