Metrizable topological vector space
In functional analysis and related areas of mathematics, a metrizable (resp. pseudometrizable) topological vector space (TVS) is a TVS whose topology is induced by a metric (resp. pseudometric). An LM-space is an inductive limit of a sequence of locally convex metrizable TVS.
(LM)-spaceAlmost open mapAuxiliary normed spaceBanach spaceBarrelled spaceBornivorous setBornological spaceBounded inverse theoremBounded operatorBounded set (topological vector space)Closed graph theorem (functional analysis)Complete topological vector spaceContinuous linear operatorDF-spaceDifferentiable vector-valued functions from Euclidean spaceDistinguished spaceDistribution (mathematics)Dual systemF-normF-seminormF-seminormsFréchet combinationFréchet spaceFréchet–Urysohn spaceHahn–Banach theoremInverse limitLM-spaceLM spaceLocally convex topological vector spaceMetrizable TVSMetrizable spaceMetrizable topological vector spaceNormed vector spaceOpen mapping theorem (functional analysis)ParanormParanormsPseudometric spacePseudometrizable TVSPseudometrizable topological vector spaceQuasi-complete space
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Metrizable topological vector space
In functional analysis and related areas of mathematics, a metrizable (resp. pseudometrizable) topological vector space (TVS) is a TVS whose topology is induced by a metric (resp. pseudometric). An LM-space is an inductive limit of a sequence of locally convex metrizable TVS.
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In functional analysis and rel ...... locally convex metrizable TVS.
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math statement
All infinite-dimensional separable complete metrizable TVS are homeomorphic.
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Every complete metrizable TVS with the Hahn-Banach extension property is locally convex.
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If is a TVS whose topology is ...... in , if then converges in .
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If is a group , is a topolog ...... placed by "open neighborhood."
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If is a pseudometrizable TVS ...... only if is complete as a TVS.
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If is a sequence in a locally ...... x combination of finitely many
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If is a topological vector sp ...... that is translation-invariant.
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If is an additive commutative ...... ausdorff and pseudometrizable.
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Let be metric on a vector sp ...... space then is a complete-TVS.
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Let be a collection of subset ...... ining the vector topology on .
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name
Banach-Saks theorem
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Continuity of addition at 0
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Mackey's countability condition
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Theorem
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note
Kalton
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Klee
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title
Proof
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In functional analysis and rel ...... locally convex metrizable TVS.
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label
Metrizable topological vector space
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