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arXiv · 2502.13587

A characterization of complete topological vector spaces with applications to spaces of measurable functions

José L. Ansorena·Alejandro Marcos
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Abstract

The aim of this paper is twofold. Firstly, we give easy-to-handle criteria to determine whether a given family of subsets of a vector space is a neighbourhood basis of the origin for a complete vector topology. Then, we apply these criteria to construct quite general complete topological vector spaces of measurable functions.

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José L. Ansorena, Alejandro Marcos. 2025-02-19. A characterization of complete topological vector spaces with applications to spaces of measurable functions. https://arxiv.org/abs/2502.13587

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