{
  "abstract": "A space is ESLC if it contains neither an $S$-space nor an $L$-space, and NFS is the class of spaces containing no free sequences of length $ω_1$. We prove that under $\\mathrm{MA}(ω_1)$, if all finite powers of $X$ belong to NFS, then $C_p(X)^ω$ is ESLC; thus, for subspaces of $C_p(X)$, hereditary Lindelöfness, hereditary separability and countable spread coincide. This is derived from a dual form of a theorem of Todorčević. A Lindelöf $Σ$-space belongs to NFS if and only if its compact subspaces have countable tightness. Hence $C_p(X)$ contains no $L$-spaces if $X$ is a Lindelöf $Σ$-space of countable tightness and $\\mathrm{MA}(ω_1)$ holds, or if $X$ is any Lindelöf $Σ$-space and PFA holds. Under $\\mathrm{MA}(ω_1)$, all iterated function spaces of Corson compact spaces are ESLC, and in ZFC the space $C_p(X,\\{0,1\\})$ is ESLC for every zero-dimensional Corson compact space $X$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04911",
  "author_total": 1,
  "authors": [
    {
      "name": "Evgenii Reznichenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dhwm3hedsd2n7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04911",
  "fulltext_url": null,
  "id": "dhwm3hedsd2n7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04911",
  "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.FA"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "arxiv",
      "math.LO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04911",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dhwm3hedsd2n7.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04911",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04911"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Hereditarily Lindelöf and hereditarily separable subspaces of function spaces",
  "title_text": "Hereditarily Lindelöf and hereditarily separable subspaces of function spaces",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/dhwm3hedsd2n7",
  "venue": "arXiv",
  "versions": []
}