A characterization of complete topological vector spaces with applications to spaces of measurable functions
arXiv:2502.13587
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.
22 pages