{
  "abstract": "For a Tychonoff space $X$ we consider the vector space $E(X)$ with basis $X$ endowed with one of the following topologies: the weak topologies $L_b(X)$ and $L_p(X)$ generated by $C_b(X)$ and $C(X)$, the free locally convex space $L(X)$, the free locally $r$-convex space $L^{(r)}(X)$ ($0<r\\le1$), the free locally pseudoconvex space $L^{(0)}(X)$, and the free topological vector space $V(X)$. We prove that $L_b(X)$ is hemicompact if and only if $X$ is finite; that for every vector topology between $L_p(X)$ and $L^{(0)}(X)$ hemicompactness is equivalent to $X$ being countable with all compact subsets finite; and that $V(X)$, as well as the free topological groups $F(X)$ and $A(X)$, are hemicompact if and only if $X$ is hemicompact. In particular, $V([0,1])$ is hemicompact, while $L([0,1])$ and $L_p([0,1])$ are not. We also describe when these spaces are $k_ω$-spaces: $L_b(X)$ and $L_p(X)$ only for finite $X$, and $L^{(r)}(X)$, $0\\le r\\le1$, only for countable discrete $X$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23020",
  "author_total": 1,
  "authors": [
    {
      "name": "Evgenii Reznichenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0h3zcm4perrza.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23020",
  "fulltext_url": null,
  "id": "0h3zcm4perrza",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23020",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GN"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7222932419",
  "pdf_url": "https://arxiv.org/pdf/2610.23020",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0h3zcm4perrza.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23020",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23020"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Hemicompactness and the $k_ω$-property of free topological vector spaces",
  "title_text": "Hemicompactness and the k_ω-property of free topological vector spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/0h3zcm4perrza",
  "venue": "arXiv",
  "versions": []
}