Weight of convex compact spaces and their boundaries

Reznichenko Evgenii

Weight of convex compact spaces and their boundaries

General Topology 2025-03-26 v1 Functional Analysis

Authors: Reznichenko Evgenii

Abstract

It is proved that if some boundary $B$ of a convex compact subset $X$ of a locally convex linear space has a countable network, then the convex compact space $X$ is metrizable. If the boundary $B$ is a Lindelof $\Sigma$ -space, then the network weight $nw(B)$ of $B$ coincides with the weight $w(K)$ of $K$ .

Keywords

convex compact spaces boundaries network weight Lindelof $\Sigma$-space metrizable

Cite

@article{arxiv.2503.19509,
  title  = {Weight of convex compact spaces and their boundaries},
  author = {Reznichenko Evgenii},
  journal= {arXiv preprint arXiv:2503.19509},
  year   = {2025}
}

Comments

in russian

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