Metrizable topological vector space
A topological vector space whose topology can be defined by a metric / From Wikipedia, the free encyclopedia
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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.