Topological vector spaces

Ptak space

A locally convex topological vector space (TVS) is B-complete or a Ptak space if every subspace is closed in the weak-* topology on (i.e. or ) whenever is closed in (when is given the subspace topology from ) for each equicontinuous subset . B-completeness is related to -completeness, where a locally convex TVS is -complete if every dense subspace is closed in whenever is closed in (when is given the subspace topology from ) for each equicontinuous subset . (Wikipedia).

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Related pages

Reflexive space | Locally convex topological vector space | Quotient space (topology) | Fréchet space | Hyperplane | Complete topological vector space | Hausdorff space | Topological vector space