Revision #849 → #1373 · back to history
addedLocally convex topological vector spaceef1e0a803d48
addedFréchet spaced6b137f4a78e
addedLocally convex TVS (via convex sets)871b00c4ab0a
addedNeighborhood basis of disks2dbc4c0254b5
addedSeminorm261258bccc85
addedNorm (from seminorm via positive definiteness)71da5105ae61
addedBase of seminorms64f1e5561ab3
addedLocally convex space (second version, via seminorms)055c923da525
addedInitial topology induced by seminormsfc63d2c6454c
addedSubbasis at the origin from seminorm preimagesf9e867ebdc5f
addedBase of continuous seminorms52635516f73e
addedSaturated family of seminorms94de5533fbb3
addedNeighborhood basis from saturated familyb8a42fd0b4b8
addedFréchet space without continuous norm — equivalence17ecbb9e07d0
addedNet convergence in locally convex spacea2e8cc4169d5
addedMinkowski functional330b31789990
addedMinkowski functional is a seminorm for balanced convex absorbing setsf346eb1df88d
addedAuxiliary normed spaces and Banach disks563ed3b23d27
addedFilter base yielding locally convex TVS topologye1a87aacab1a
addedSeparated/total family of seminorms86f108b4a644
addedHausdorff iff separated family of seminorms5e5fee71aa2e
addedPseudometrizability via countable family of seminormsb705bba49459
addedCauchy net in a locally convex space988775a10099
addedDirected family of seminormsdfffe8f635bb
addedEquivalent directed family exists923ffd7d9488
addedSeminormability and normability criteria3fe6a8fb9047
addedSeminormable iff bounded neighborhood of originc59418551f43
addedExtension property and Hahn-Banach extension property (HBEP)7af74fcab385
addedHahn–Banach implies HBEP for Hausdorff locally convex90e3a93991f7
addedUncountable-dim space with finest vector topology has HBEP964e725008ad
addedKalton: complete metrizable TVS with HBEP is locally convex8a9c449b5ba8
addedClosure characterization in locally convex space54245543db05
addedHausdorff LCS embeds in product of Banach spacesbd95ce317d94
addedAnderson–Kadec theorembc69589602dc
addedConvexity criterion via Minkowski sumsafeef5696210
addedStar-shapedness of convex sets containing origincc20d7323417
addedMinkowski sum and scalar multiples of convex sets are convex5e8476956f44
addedOpen convex subsets via sublinear functionals6b744561d6ff
addedInterior and closure of convex set are convexbd628fb5dc35
addedInterior/closure agreement for convex set with non-empty interior8e5442b58ed9
addedOpen line segment from interior to closure lies in interior3310ad4e2b99
addedSeparating a vector from a closed subspace by convex neighborhood2e4947f18806
addedClosure of convex set invariant under compatible topologiesb4eae753c5ff
addedConvex and disked hull of totally bounded sets are totally bounded9ebc70ede280
addedConvex/disked hull of compact set is compact in complete LCSc8667c0b0cbf
addedConvex hull of bounded set is bounded in LCS92e98cbe7931
addedClosed convex hull of compact set is compact in Fréchet spacedd29e7335930
addedLinear combinations of totally bounded sets are totally bounded86180cad7f84
addedConvex hull and related hullsfc76f5eda8f2
addedConvex hull of compact set in Hilbert space need not be closed1b8941bffe4a
addedClosed convex hull is precompact in Hausdorff LCS3d7bdfeb9510
addedClosure of convex hull of compact set in quasi-complete LCSd12b11a30932
addedConvex hull of precompact set is precompact265e94fa2707
addedConvex hull of finite union of compact convex sets is compact3fa334e09f48
addedBipolar theoremdf46c2ad65fe
addedBalanced hull of convex set need not be convex705944a4f901
addedConvex combination representation for intersecting convex sets5a6e46d5a2b2
addedConvex balanced hullc4997f316aa6
addedConvex balanced hull equals convex hull of balanced hull3502a117007f
addedClosed convex hulls compact implies sum closed convex hull compacte05ddb0570e4
addedCarathéodory's theorem550323fd33d2
addedTrivial (indiscrete) topology as coarsest locally convex TVSc726c57daacd
addedFinest locally convex topologyfdd6ba6999d9
addedProperties of the finest locally convex topology4d593419db4f
addedNormed spaces and Banach spaces as locally convexbc9fb795c9d5
addedFréchet spaces as locally convex6ea578f4376c
addedSpace of real-valued sequences as Fréchet spacecd68a116b597
addedWeak topology from collection of linear functionals2e36cf81b69c
addedSchwartz space60c0d20e8f2f
addedSpace of smooth compactly supported functions / LF space2e921924f890
addedContinuous functions with topology of uniform convergence on compacts666e45452582
addedLp spaces for 0<p<1 lack local convexitye5ad26a56889
addedSpace of measurable functions with convergence in measurec40a8d115410
addedContinuity criterion for linear maps via seminorms589c79830dde
addedContinuity of linear operator into locally convex TVSd50b8306d728
addedLinear functional bounded by seminorm criterion36f5f7fa1a94
addedContinuity criterion for multilinear mapsee25e4e8e8e2