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If the spaces are not locally convex, then there is a notion of web where the requirement of being a disk is replaced by the requirement of being
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is a webbed space, then any
Hausdorff locally convex topology weaker than this (webbed) topology is also webbed.
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862:{\displaystyle D_{ijk}\subseteq \left({\tfrac {1}{2}}\right)D_{ij}\quad {\text{ for every }}k}
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479:{\displaystyle D_{ij}\subseteq \left({\tfrac {1}{2}}\right)D_{i}\quad {\text{ for every }}j}
47:
whose codomains are webbed spaces. A space is called webbed if there exists a collection of
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is a sequence of disks, with the first disk being selected from the first stratum, say
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1952: â A locally convex topological vector space that is also a complete metric space
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1976: â Generalization of closed graph, open mapping, and uniform boundedness theorem
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2237:. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer.
1918:
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758:
satisfying analogously defined properties; explicitly, this means that for every
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topological vector spaces into a webbed topological vector space is continuous.
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1728:
Any continuous surjective linear map from a webbed locally convex space onto an
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Any continuous surjective linear map from a webbed locally convex space onto an
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1443:
The continuous dual space of a metrizable locally convex space endowed with the
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2203:. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press.
1946: â Topological vector space with a complete translation-invariant metric
55:
that satisfies certain properties. Webs were first investigated by de Wilde.
3347:
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2168:
1964: â A topological vector space whose topology can be defined by a metric
1906: â Map that satisfies a condition similar to that of being an open map.
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and the second being selected from the sequence that was associated with
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1943:
2149:. Mathematical Surveys and Monographs. Vol. 53. Providence, R.I:
2068:
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1474:
of a denumerable family of locally convex metrizable spaces, then the
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satisfying the following absorbency and convergence requirements.
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2021:
2019:
2006:
2004:
2002:
2747:
2263:
1016:{\displaystyle \left(D_{ijk}\right)_{i,j,k\in \mathbb {N} }}
1930: â Theorems connecting continuity to closure of graphs
1590:(meaning that its graph is a sequentially closed subset of
1879:. For such a notion of web we have the following results:
1183:
and so on. We also require that if a sequence of vectors
618:{\displaystyle \left(D_{ij}\right)_{i,j\in \mathbb {N} }}
1412:
A sequentially closed vector subspace of a webbed space.
1923:
Pages displaying short descriptions of redirect targets
1908:
Pages displaying short descriptions of redirect targets
16:
Space where open mapping and closed graph theorems hold
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35:
designed with the goal of allowing the results of the
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1958: â Fixed-point theorem for set-valued functions
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belonging to the second, and so on) then the series
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299:in the first stratum, there must exists a sequence
2619:Spectral theory of ordinary differential equations
1970: â Condition for a linear operator to be open
1921: â Graph of a map closed in the product space
1889:Any closed linear map from the inductive limit of
1863:
1831:
1807:
1787:
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1702:into a webbed locally convex space is continuous.
1695:Any closed linear map from the inductive limit of
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1993:
235:{\displaystyle \bigcup _{i\in \mathbb {N} }D_{i}}
913:{\displaystyle \cup _{k\in \mathbb {N} }D_{ijk}}
2106:. Vol. 936. Berlin, Heidelberg, New York:
1664:or an inductive limit of Fréchet spaces), then
1384:if and only if it is both a webbed space and a
731:{\displaystyle D_{ij1},D_{ij2},D_{ij3},\ldots }
661:in the second stratum, assign another sequence
527:{\displaystyle \cup _{j\in \mathbb {N} }D_{ij}}
114:: The first stratum must consist of a sequence
2199:Narici, Lawrence; Beckenstein, Edward (2011).
2759:
2275:
8:
2100:Counterexamples in Topological Vector Spaces
360:{\displaystyle D_{i1},D_{i2},D_{i3},\ldots }
1883:
1737:
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1548:
1347:
1243:belonging to the first disk in the strand,
2766:
2752:
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2310:
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2268:
2260:
2176:Kriegl, Andreas; Michor, Peter W. (1997).
1968:Open mapping theorem (functional analysis)
1928:Closed graph theorem (functional analysis)
1328:on which a web can be defined is called a
1311:{\displaystyle \sum _{n=1}^{\infty }x_{n}}
2178:The Convenient Setting of Global Analysis
2143:The Convenient Setting of Global Analysis
1844:
1824:
1800:
1780:
1748:
1743:If the image of a closed linear operator
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1062:That is, use induction to define stratum
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166:{\displaystyle D_{1},D_{2},D_{3},\ldots }
151:
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125:
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68:
2572:Group algebra of a locally compact group
1915: â Type of topological vector space
1717:of Baire locally convex spaces is open.
1392:All of the following spaces are webbed:
2180:. Mathematical Surveys and Monographs.
2091:Closed graph theorems and webbed spaces
1986:
1422:A Hausdorff quotient of a webbed space.
1326:locally convex topological vector space
1027:Continue this process to define strata
2905:Uniform boundedness (BanachâSteinhaus)
1586:be a linear map between TVSs that is
7:
1795:into Hausdorff locally convex space
1425:The image of a webbed space under a
1962:Metrizable topological vector space
1342:Examples and sufficient conditions
1293:
14:
1775:from locally convex webbed space
3443:
3442:
2728:
2727:
2654:Topological quantum field theory
1216:is selected from a strand (with
3430:With the approximation property
850:
467:
2893:Open mapping (BanachâSchauder)
1855:
1759:
1570:
1409:of sequences of webbed spaces.
1203:
1190:
103:is a stratified collection of
1:
2450:Uniform boundedness principle
2182:American Mathematical Society
2151:American Mathematical Society
2073:Narici & Beckenstein 2011
2056:Narici & Beckenstein 2011
2044:Narici & Beckenstein 2011
2032:Narici & Beckenstein 2011
2011:Narici & Beckenstein 2011
1994:Narici & Beckenstein 2011
625:will form the second stratum.
43:to hold for a wider class of
2229:; Wolff, Manfred P. (1999).
2104:Lecture Notes in Mathematics
1956:Kakutani fixed-point theorem
1429:linear map if that image is
1055:{\displaystyle 4,5,\ldots .}
3114:Radially convex/Star-shaped
3099:Pre-compact/Totally bounded
2098:Khaleelulla, S. M. (1982).
3490:
2800:Continuous linear operator
2593:Invariant subspace problem
1871:is a surjective open map.
3474:Topological vector spaces
3438:
3145:Algebraic interior (core)
2887:Vector-valued HahnâBanach
2775:Topological vector spaces
2723:
2313:
2231:Topological Vector Spaces
2201:Topological Vector Spaces
1609:{\displaystyle X\times Y}
2975:Topological homomorphism
2835:Topological vector space
2562:Spectrum of a C*-algebra
1939:Discontinuous linear map
1864:{\displaystyle A:X\to Y}
1768:{\displaystyle A:X\to Y}
1579:{\displaystyle A:X\to Y}
1359:topological vector space
91:topological vector space
33:topological vector space
2659:Noncommutative geometry
2089:De Wilde, Marc (1978).
1730:ultrabornological space
1658:ultrabornological space
1427:sequentially continuous
1209:{\displaystyle (x_{n})}
1023:form the third stratum.
948:{\displaystyle D_{ij}.}
784:{\displaystyle D_{i,j}}
3033:Absolutely convex/disk
2715:TomitaâTakesaki theory
2690:Approximation property
2634:Calculus of variations
1934:Closed linear operator
1904:Almost open linear map
1865:
1833:
1809:
1789:
1769:
1678:
1650:
1636:is a webbed space and
1630:
1610:
1580:
1532:
1505:So in particular, the
1492:
1472:strict inductive limit
1464:
1374:
1312:
1297:
1264:
1237:
1210:
1177:
1176:{\displaystyle D_{i},}
1147:
1146:{\displaystyle D_{i},}
1105:
1082:
1056:
1017:
949:
914:
863:
785:
752:
732:
655:
654:{\displaystyle D_{ij}}
619:
560:
559:{\displaystyle D_{i}.}
528:
480:
408:
381:
361:
293:
261:
236:
197:such that their union
191:
167:
77:
3068:Complemented subspace
2882:hyperplane separation
2710:BanachâMazur distance
2673:Generalized functions
1866:
1834:
1810:
1790:
1770:
1700:locally convex spaces
1679:
1651:
1631:
1611:
1581:
1533:
1493:
1476:continuous dual space
1465:
1375:
1313:
1277:
1265:
1263:{\displaystyle x_{2}}
1238:
1236:{\displaystyle x_{1}}
1211:
1178:
1148:
1106:
1083:
1057:
1018:
950:
915:
864:
853: for every
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561:
529:
481:
470: for every
409:
407:{\displaystyle D_{i}}
382:
362:
294:
292:{\displaystyle D_{i}}
262:
237:
192:
168:
78:
3318:Locally convex space
2868:Closed graph theorem
2820:Locally convex space
2455:Kakutani fixed-point
2440:Riesz representation
2184:. pp. 557â578.
1884:Closed Graph Theorem
1843:
1823:
1799:
1779:
1747:
1738:Open Mapping Theorem
1723:Open Mapping Theorem
1708:Open Mapping Theorem
1690:Closed Graph Theorem
1668:
1640:
1620:
1594:
1558:
1549:Closed Graph Theorem
1522:
1482:
1454:
1445:strong dual topology
1364:
1274:
1247:
1220:
1187:
1157:
1127:
1092:
1088:in terms of stratum
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959:
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795:
762:
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665:
635:
570:
540:
490:
418:
391:
387:such that for every
371:
303:
276:
248:
201:
181:
118:
67:
41:closed graph theorem
37:open mapping theorem
3469:Functional analysis
3298:Interpolation space
2830:Operator topologies
2639:Functional calculus
2598:Mahler's conjecture
2577:Von Neumann algebra
2291:Functional analysis
2227:Schaefer, Helmut H.
2075:, pp. 474â476.
2058:, pp. 459â483.
1887: —
1741: —
1726: —
1711: —
1693: —
1588:sequentially closed
1552: —
1355: —
1081:{\displaystyle n+1}
25:functional analysis
3328:(Pseudo)Metrizable
3160:Minkowski addition
3012:Sublinear function
2664:Riemann hypothesis
2363:Topological vector
1996:, p. 470â471.
1885:
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1709:
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1509:of locally convex
1488:
1460:
1440:of a webbed space.
1370:
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1104:{\displaystyle n.}
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404:
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289:
260:{\displaystyle X.}
257:
232:
221:
187:
163:
73:
23:, particularly in
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3455:
3175:Relative interior
2921:Bilinear operator
2805:Linear functional
2741:
2740:
2644:Integral operator
2421:
2420:
2244:978-1-4612-7155-0
2160:978-0-8218-0780-4
2117:978-3-540-11565-6
2093:. London: Pitman.
1832:{\displaystyle Y}
1808:{\displaystyle Y}
1788:{\displaystyle X}
1677:{\displaystyle A}
1649:{\displaystyle X}
1629:{\displaystyle Y}
1531:{\displaystyle X}
1511:metrizable spaces
1491:{\displaystyle X}
1463:{\displaystyle X}
1438:bornologification
1419:of webbed spaces.
1403:Projective limits
1373:{\displaystyle X}
854:
830:
751:{\displaystyle X}
471:
450:
380:{\displaystyle X}
204:
190:{\displaystyle X}
76:{\displaystyle X}
3481:
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3420:Uniformly smooth
3089:
3081:
3048:Balanced/Circled
3038:Absorbing/Radial
2768:
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2649:Jones polynomial
2567:Operator algebra
2311:
2284:
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2172:
2148:
2138:Michor, Peter W.
2129:
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1407:inductive limits
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272:: For each disk
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230:
220:
219:
196:
194:
193:
188:
172:
170:
169:
164:
156:
155:
143:
142:
130:
129:
100:
99:
82:
80:
79:
74:
3489:
3488:
3484:
3483:
3482:
3480:
3479:
3478:
3459:
3458:
3457:
3452:
3434:
3196:B-complete/Ptak
3179:
3123:
3087:
3079:
3058:Bounding points
3021:
2963:Densely defined
2909:
2898:Bounded inverse
2844:
2778:
2772:
2742:
2737:
2719:
2683:Advanced topics
2678:
2602:
2581:
2540:
2506:HilbertâSchmidt
2479:
2470:GelfandâNaimark
2417:
2367:
2302:
2288:
2245:
2225:
2211:
2198:
2192:
2175:
2161:
2146:
2134:Kriegl, Andreas
2132:
2118:
2108:Springer-Verlag
2097:
2088:
2085:
2080:
2079:
2071:
2062:
2054:
2050:
2042:
2038:
2030:
2017:
2009:
2000:
1992:
1988:
1983:
1974:Ursescu theorem
1922:
1913:Barrelled space
1907:
1900:
1895:
1886:
1873:
1841:
1840:
1821:
1820:
1797:
1796:
1777:
1776:
1745:
1744:
1740:
1734:
1725:
1719:
1715:inductive limit
1710:
1704:
1692:
1686:
1684:is continuous.
1666:
1665:
1638:
1637:
1618:
1617:
1592:
1591:
1556:
1555:
1551:
1545:
1520:
1519:
1500:strong topology
1480:
1479:
1452:
1451:
1390:
1362:
1361:
1354:
1352:(de Wilde 1978)
1351:
1344:
1332:
1331:
1298:
1272:
1271:
1250:
1245:
1244:
1223:
1218:
1217:
1193:
1185:
1184:
1160:
1155:
1154:
1130:
1125:
1124:
1117:
1116:
1090:
1089:
1064:
1063:
1029:
1028:
967:
963:
962:
957:
956:
929:
924:
923:
894:
876:
871:
870:
837:
817:
798:
793:
792:
765:
760:
759:
740:
739:
706:
687:
668:
663:
662:
638:
633:
632:
631:: To each disk
578:
574:
573:
568:
567:
543:
538:
537:
511:
493:
488:
487:
457:
437:
421:
416:
415:
394:
389:
388:
369:
368:
338:
322:
306:
301:
300:
279:
274:
273:
246:
245:
222:
199:
198:
179:
178:
147:
134:
121:
116:
115:
97:
96:
65:
64:
61:
17:
12:
11:
5:
3487:
3485:
3477:
3476:
3471:
3461:
3460:
3454:
3453:
3451:
3450:
3439:
3436:
3435:
3433:
3432:
3427:
3422:
3417:
3415:Ultrabarrelled
3407:
3401:
3396:
3390:
3385:
3380:
3375:
3370:
3365:
3356:
3350:
3345:
3343:Quasi-complete
3340:
3338:Quasibarrelled
3335:
3330:
3325:
3320:
3315:
3310:
3305:
3300:
3295:
3290:
3285:
3280:
3279:
3278:
3268:
3263:
3258:
3253:
3248:
3243:
3238:
3233:
3228:
3218:
3213:
3203:
3198:
3193:
3187:
3185:
3181:
3180:
3178:
3177:
3167:
3162:
3157:
3152:
3147:
3137:
3131:
3129:
3128:Set operations
3125:
3124:
3122:
3121:
3116:
3111:
3106:
3101:
3096:
3091:
3083:
3075:
3070:
3065:
3060:
3055:
3050:
3045:
3040:
3035:
3029:
3027:
3023:
3022:
3020:
3019:
3014:
3009:
3004:
2999:
2998:
2997:
2992:
2987:
2977:
2972:
2971:
2970:
2965:
2960:
2955:
2950:
2945:
2940:
2930:
2929:
2928:
2917:
2915:
2911:
2910:
2908:
2907:
2902:
2901:
2900:
2890:
2884:
2875:
2870:
2865:
2863:BanachâAlaoglu
2860:
2858:AndersonâKadec
2854:
2852:
2846:
2845:
2843:
2842:
2837:
2832:
2827:
2822:
2817:
2812:
2807:
2802:
2797:
2792:
2786:
2784:
2783:Basic concepts
2780:
2779:
2773:
2771:
2770:
2763:
2756:
2748:
2739:
2738:
2736:
2735:
2724:
2721:
2720:
2718:
2717:
2712:
2707:
2702:
2700:Choquet theory
2697:
2692:
2686:
2684:
2680:
2679:
2677:
2676:
2666:
2661:
2656:
2651:
2646:
2641:
2636:
2631:
2626:
2621:
2616:
2610:
2608:
2604:
2603:
2601:
2600:
2595:
2589:
2587:
2583:
2582:
2580:
2579:
2574:
2569:
2564:
2559:
2554:
2552:Banach algebra
2548:
2546:
2542:
2541:
2539:
2538:
2533:
2528:
2523:
2518:
2513:
2508:
2503:
2498:
2493:
2487:
2485:
2481:
2480:
2478:
2477:
2475:BanachâAlaoglu
2472:
2467:
2462:
2457:
2452:
2447:
2442:
2437:
2431:
2429:
2423:
2422:
2419:
2418:
2416:
2415:
2410:
2405:
2403:Locally convex
2400:
2386:
2381:
2375:
2373:
2369:
2368:
2366:
2365:
2360:
2355:
2350:
2345:
2340:
2335:
2330:
2325:
2320:
2314:
2308:
2304:
2303:
2289:
2287:
2286:
2279:
2272:
2264:
2258:
2257:
2243:
2223:
2210:978-1584888666
2209:
2196:
2190:
2173:
2159:
2130:
2116:
2095:
2084:
2081:
2078:
2077:
2060:
2048:
2046:, p. 473.
2036:
2034:, p. 481.
2015:
2013:, p. 472.
1998:
1985:
1984:
1982:
1979:
1978:
1977:
1971:
1965:
1959:
1953:
1947:
1941:
1936:
1931:
1925:
1916:
1910:
1899:
1896:
1881:
1860:
1857:
1854:
1851:
1848:
1828:
1804:
1784:
1764:
1761:
1758:
1755:
1752:
1735:
1720:
1705:
1687:
1673:
1645:
1625:
1605:
1602:
1599:
1575:
1572:
1569:
1566:
1563:
1546:
1544:
1541:
1540:
1539:
1527:
1516:
1515:
1514:
1487:
1459:
1448:
1441:
1434:
1423:
1420:
1413:
1410:
1400:
1397:Fréchet spaces
1369:
1345:
1343:
1340:
1336:
1305:
1301:
1295:
1290:
1287:
1284:
1280:
1257:
1253:
1230:
1226:
1205:
1200:
1196:
1192:
1172:
1167:
1163:
1142:
1137:
1133:
1121:
1100:
1097:
1077:
1074:
1071:
1051:
1048:
1045:
1042:
1039:
1036:
1025:
1024:
1009:
1005:
1002:
999:
996:
993:
990:
985:
980:
977:
974:
970:
966:
944:
939:
936:
932:
907:
904:
901:
897:
890:
886:
883:
879:
858:
847:
844:
840:
835:
829:
826:
820:
816:
811:
808:
805:
801:
778:
775:
772:
768:
747:
727:
724:
719:
716:
713:
709:
705:
700:
697:
694:
690:
686:
681:
678:
675:
671:
648:
645:
641:
626:
611:
607:
604:
601:
598:
593:
588:
585:
581:
577:
555:
550:
546:
521:
518:
514:
507:
503:
500:
496:
475:
464:
460:
455:
449:
446:
440:
436:
431:
428:
424:
401:
397:
376:
356:
353:
348:
345:
341:
337:
332:
329:
325:
321:
316:
313:
309:
286:
282:
267:
256:
253:
229:
225:
218:
214:
211:
207:
186:
162:
159:
154:
150:
146:
141:
137:
133:
128:
124:
101:
88:locally convex
72:
60:
57:
15:
13:
10:
9:
6:
4:
3:
2:
3486:
3475:
3472:
3470:
3467:
3466:
3464:
3449:
3441:
3440:
3437:
3431:
3428:
3426:
3423:
3421:
3418:
3416:
3412:
3408:
3406:) convex
3405:
3402:
3400:
3397:
3395:
3391:
3389:
3386:
3384:
3381:
3379:
3378:Semi-complete
3376:
3374:
3371:
3369:
3366:
3364:
3360:
3357:
3355:
3351:
3349:
3346:
3344:
3341:
3339:
3336:
3334:
3331:
3329:
3326:
3324:
3321:
3319:
3316:
3314:
3311:
3309:
3306:
3304:
3301:
3299:
3296:
3294:
3293:Infrabarreled
3291:
3289:
3286:
3284:
3281:
3277:
3274:
3273:
3272:
3269:
3267:
3264:
3262:
3259:
3257:
3254:
3252:
3251:Distinguished
3249:
3247:
3244:
3242:
3239:
3237:
3234:
3232:
3229:
3227:
3223:
3219:
3217:
3214:
3212:
3208:
3204:
3202:
3199:
3197:
3194:
3192:
3189:
3188:
3186:
3184:Types of TVSs
3182:
3176:
3172:
3168:
3166:
3163:
3161:
3158:
3156:
3153:
3151:
3148:
3146:
3142:
3138:
3136:
3133:
3132:
3130:
3126:
3120:
3117:
3115:
3112:
3110:
3107:
3105:
3104:Prevalent/Shy
3102:
3100:
3097:
3095:
3094:Extreme point
3092:
3090:
3084:
3082:
3076:
3074:
3071:
3069:
3066:
3064:
3061:
3059:
3056:
3054:
3051:
3049:
3046:
3044:
3041:
3039:
3036:
3034:
3031:
3030:
3028:
3026:Types of sets
3024:
3018:
3015:
3013:
3010:
3008:
3005:
3003:
3000:
2996:
2993:
2991:
2988:
2986:
2983:
2982:
2981:
2978:
2976:
2973:
2969:
2968:Discontinuous
2966:
2964:
2961:
2959:
2956:
2954:
2951:
2949:
2946:
2944:
2941:
2939:
2936:
2935:
2934:
2931:
2927:
2924:
2923:
2922:
2919:
2918:
2916:
2912:
2906:
2903:
2899:
2896:
2895:
2894:
2891:
2888:
2885:
2883:
2879:
2876:
2874:
2871:
2869:
2866:
2864:
2861:
2859:
2856:
2855:
2853:
2851:
2847:
2841:
2838:
2836:
2833:
2831:
2828:
2826:
2825:Metrizability
2823:
2821:
2818:
2816:
2813:
2811:
2810:Fréchet space
2808:
2806:
2803:
2801:
2798:
2796:
2793:
2791:
2788:
2787:
2785:
2781:
2776:
2769:
2764:
2762:
2757:
2755:
2750:
2749:
2746:
2734:
2726:
2725:
2722:
2716:
2713:
2711:
2708:
2706:
2705:Weak topology
2703:
2701:
2698:
2696:
2693:
2691:
2688:
2687:
2685:
2681:
2674:
2670:
2667:
2665:
2662:
2660:
2657:
2655:
2652:
2650:
2647:
2645:
2642:
2640:
2637:
2635:
2632:
2630:
2629:Index theorem
2627:
2625:
2622:
2620:
2617:
2615:
2612:
2611:
2609:
2605:
2599:
2596:
2594:
2591:
2590:
2588:
2586:Open problems
2584:
2578:
2575:
2573:
2570:
2568:
2565:
2563:
2560:
2558:
2555:
2553:
2550:
2549:
2547:
2543:
2537:
2534:
2532:
2529:
2527:
2524:
2522:
2519:
2517:
2514:
2512:
2509:
2507:
2504:
2502:
2499:
2497:
2494:
2492:
2489:
2488:
2486:
2482:
2476:
2473:
2471:
2468:
2466:
2463:
2461:
2458:
2456:
2453:
2451:
2448:
2446:
2443:
2441:
2438:
2436:
2433:
2432:
2430:
2428:
2424:
2414:
2411:
2409:
2406:
2404:
2401:
2398:
2394:
2390:
2387:
2385:
2382:
2380:
2377:
2376:
2374:
2370:
2364:
2361:
2359:
2356:
2354:
2351:
2349:
2346:
2344:
2341:
2339:
2336:
2334:
2331:
2329:
2326:
2324:
2321:
2319:
2316:
2315:
2312:
2309:
2305:
2300:
2296:
2292:
2285:
2280:
2278:
2273:
2271:
2266:
2265:
2262:
2254:
2250:
2246:
2240:
2236:
2232:
2228:
2224:
2220:
2216:
2212:
2206:
2202:
2197:
2193:
2191:9780821807804
2187:
2183:
2179:
2174:
2170:
2166:
2162:
2156:
2152:
2145:
2144:
2139:
2135:
2131:
2127:
2123:
2119:
2113:
2109:
2105:
2101:
2096:
2092:
2087:
2086:
2082:
2074:
2069:
2067:
2065:
2061:
2057:
2052:
2049:
2045:
2040:
2037:
2033:
2028:
2026:
2024:
2022:
2020:
2016:
2012:
2007:
2005:
2003:
1999:
1995:
1990:
1987:
1980:
1975:
1972:
1969:
1966:
1963:
1960:
1957:
1954:
1951:
1950:Fréchet space
1948:
1945:
1942:
1940:
1937:
1935:
1932:
1929:
1926:
1920:
1917:
1914:
1911:
1905:
1902:
1901:
1897:
1894:
1892:
1880:
1878:
1872:
1858:
1852:
1849:
1846:
1826:
1818:
1802:
1782:
1762:
1756:
1753:
1750:
1733:
1731:
1718:
1716:
1703:
1701:
1698:
1685:
1671:
1663:
1662:Fréchet space
1659:
1643:
1623:
1603:
1600:
1597:
1589:
1573:
1567:
1564:
1561:
1542:
1525:
1517:
1512:
1508:
1504:
1503:
1501:
1485:
1477:
1473:
1457:
1449:
1446:
1442:
1439:
1435:
1432:
1428:
1424:
1421:
1418:
1414:
1411:
1408:
1404:
1401:
1398:
1395:
1394:
1393:
1389:
1387:
1383:
1382:Fréchet space
1367:
1360:
1341:
1339:
1337:
1330:
1327:
1324:
1319:
1303:
1299:
1288:
1285:
1282:
1278:
1255:
1251:
1228:
1224:
1198:
1194:
1170:
1165:
1161:
1140:
1135:
1131:
1122:
1115:
1111:
1098:
1095:
1075:
1072:
1069:
1049:
1046:
1043:
1040:
1037:
1034:
1003:
1000:
997:
994:
991:
988:
983:
978:
975:
972:
968:
964:
942:
937:
934:
930:
922:
905:
902:
899:
895:
884:
881:
877:
856:
845:
842:
838:
833:
827:
824:
818:
814:
809:
806:
803:
799:
776:
773:
770:
766:
745:
725:
722:
717:
714:
711:
707:
703:
698:
695:
692:
688:
684:
679:
676:
673:
669:
646:
643:
639:
630:
627:
605:
602:
599:
596:
591:
586:
583:
579:
575:
553:
548:
544:
536:
519:
516:
512:
501:
498:
494:
473:
462:
458:
453:
447:
444:
438:
434:
429:
426:
422:
399:
395:
374:
354:
351:
346:
343:
339:
335:
330:
327:
323:
319:
314:
311:
307:
284:
280:
271:
268:
254:
251:
244:
227:
223:
212:
209:
205:
184:
176:
160:
157:
152:
148:
144:
139:
135:
131:
126:
122:
113:
110:
109:
108:
106:
102:
95:
92:
89:
86:
70:
58:
56:
54:
50:
46:
42:
38:
34:
30:
26:
22:
3424:
3354:Polynomially
3283:Grothendieck
3276:tame Fréchet
3226:Bornological
3086:Linear cone
3078:Convex cone
3053:Banach disks
2995:Sesquilinear
2850:Main results
2840:Vector space
2795:Completeness
2790:Banach space
2695:Balanced set
2669:Distribution
2607:Applications
2460:KreinâMilman
2445:Closed graph
2230:
2200:
2177:
2142:
2099:
2090:
2051:
2039:
1989:
1919:Closed graph
1882:
1874:
1736:
1721:
1706:
1688:
1547:
1507:strong duals
1391:
1346:
1333:webbed space
1329:
1320:
1114:
1112:
1026:
738:of disks in
628:
367:of disks in
269:
111:
94:
62:
52:
29:webbed space
28:
18:
3348:Quasinormed
3261:FK-AK space
3155:Linear span
3150:Convex hull
3135:Affine hull
2938:Almost open
2878:HahnâBanach
2624:Heat kernel
2614:Hardy space
2521:Trace class
2435:HahnâBanach
2397:Topological
1660:(such as a
1513:are webbed.
1502:is webbed.
1386:Baire space
1318:converges.
51:, called a
45:linear maps
21:mathematics
3463:Categories
3388:Stereotype
3246:(DF)-space
3241:Convenient
2980:Functional
2948:Continuous
2933:Linear map
2873:F. Riesz's
2815:Linear map
2557:C*-algebra
2372:Properties
2083:References
1447:is webbed.
1415:Countable
3404:Uniformly
3363:Reflexive
3211:Barrelled
3207:Countably
3119:Symmetric
3017:Transpose
2531:Unbounded
2526:Transpose
2484:Operators
2413:Separable
2408:Reflexive
2393:Algebraic
2379:Barrelled
2253:840278135
2219:144216834
1981:Citations
1856:→
1817:nonmeager
1760:→
1732:is open.
1601:×
1571:→
1498:with the
1431:Hausdorff
1323:Hausdorff
1294:∞
1279:∑
1047:…
1004:∈
955:The sets
885:∈
878:∪
815:⊆
726:…
629:Stratum 3
606:∈
566:The sets
502:∈
495:∪
435:⊆
355:…
270:Stratum 2
213:∈
206:⋃
161:…
112:Stratum 1
85:Hausdorff
3448:Category
3399:Strictly
3373:Schwartz
3313:LF-space
3308:LB-space
3266:FK-space
3236:Complete
3216:BK-space
3141:Relative
3088:(subset)
3080:(subset)
3007:Seminorm
2990:Bilinear
2733:Category
2545:Algebras
2427:Theorems
2384:Complete
2353:Schwartz
2299:glossary
2169:37141279
2140:(1997).
1898:See also
1877:balanced
1543:Theorems
1417:products
39:and the
3413:)
3361:)
3303:K-space
3288:Hilbert
3271:Fréchet
3256:F-space
3231:Brauner
3224:)
3209:)
3191:Asplund
3173:)
3143:)
3063:Bounded
2958:Compact
2943:Bounded
2880: (
2536:Unitary
2516:Nuclear
2501:Compact
2496:Bounded
2491:Adjoint
2465:Minâmax
2358:Sobolev
2343:Nuclear
2333:Hilbert
2328:Fréchet
2293: (
2126:8588370
1944:F-space
1616:). If
1470:is the
1348:Theorem
921:absorbs
535:absorbs
243:absorbs
3425:Webbed
3411:Quasi-
3333:Montel
3323:Mackey
3222:Ultra-
3201:Banach
3109:Radial
3073:Convex
3043:Affine
2985:Linear
2953:Closed
2777:(TVSs)
2511:Normal
2348:Orlicz
2338:Hölder
2318:Banach
2307:Spaces
2295:topics
2251:
2241:
2217:
2207:
2188:
2167:
2157:
2124:
2114:
1656:is an
1350:
1118:strand
3383:Smith
3368:Riesz
3359:Semi-
3171:Quasi
3165:Polar
2323:Besov
2147:(PDF)
1891:Baire
1839:then
1697:Baire
1380:is a
175:disks
105:disks
83:be a
31:is a
3002:Norm
2926:form
2914:Maps
2671:(or
2389:Dual
2249:OCLC
2239:ISBN
2215:OCLC
2205:ISBN
2186:ISBN
2165:OCLC
2155:ISBN
2122:OCLC
2112:ISBN
1554:Let
1436:The
1405:and
869:and
486:and
93:. A
63:Let
49:sets
27:, a
2235:GTM
1819:in
1815:is
1518:If
1478:of
1450:If
177:in
173:of
98:web
59:Web
53:web
19:In
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2247:.
2233:.
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2136:;
2120:.
2110:.
2102:.
2063:^
2018:^
2001:^
1388:.
1357:A
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1672:A
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1070:n
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1041:5
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1035:4
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