Weight of convex compact spaces and their boundaries
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910892591939584 |
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| author | Evgenii, Reznichenko |
| author_facet | Evgenii, Reznichenko |
| contents | 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 $Σ$-space, then the network weight $nw(B)$ of $B$ coincides with the weight $w(K)$ of $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19509 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weight of convex compact spaces and their boundaries Evgenii, Reznichenko General Topology Functional Analysis 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 $Σ$-space, then the network weight $nw(B)$ of $B$ coincides with the weight $w(K)$ of $K$. |
| title | Weight of convex compact spaces and their boundaries |
| topic | General Topology Functional Analysis |
| url | https://arxiv.org/abs/2503.19509 |