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Reference.org
Metrizable topological vector space
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<p>In <a href="/facts/Functional_analysis/MIp233MT">functional analysis</a> and related areas of <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a metrizable (resp. pseudometrizable) <a href="/facts/Topological_vector_space/XRex1ChN">topological vector space</a> (TVS) is a TVS whose topology is induced by a metric (resp. <a href="/facts/Pseudometric_space/uy1o2lhk">pseudometric</a>). An LM-space is an <a href="/facts/Inductive_limit/V3JuHnYK">inductive limit</a> of a sequence of <a href="/facts/Locally_convex/AGrPrayC">locally convex</a> metrizable TVS. </p>