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arXiv · 2503.19509

Weight of convex compact spaces and their boundaries

Reznichenko Evgenii
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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 $K$.

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Reznichenko Evgenii. 2025-03-25. Weight of convex compact spaces and their boundaries. https://arxiv.org/abs/2503.19509

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