The strongest vector space topology is locally convex on separable linear subspaces

ArticleOriginal scientific text

Title

Authors ¹

Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 137, 00-950 Warszawa, Poland

Let X be a real or complex vector space equipped with the strongest vector space topology

τ_{max}

. Besides the result announced in the title we prove that X is uncountable-dimensional if and only if it is not locally pseudoconvex.

topological vector spaces, locally pseudoconvex spaces, locally convex subspaces

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