{
  "abstract": "For any Tychonoff space $X$, let $D(X)$ denote either the space $C(X)$ of all continuous real-valued functions on $X$ or the space $C^*(X)$ of all bounded continuous real-valued functions on $X$. We write $D_p(X)$ when $D(X)$ is endowed with the topology of pointwise convergence. In our recently published paper [8, Theorem 1.6], we obtained the following result: if $T: D_{p}(X) \\to D_{p}(Y)$ is a linear continuous surjection, where $X$ is a metrizable space and $Y$ is a perfectly normal space, then $Y$ inherits a given topological property $\\mathcal{P}$ from $X$. A linear continuous surjection $T: E_{p}(X)\\to E_{p}(Y)$ is said to be densely defined if $E(X)$ and $E(Y)$ are dense linear subspaces of $D_{p}(X)$ and $D_{p}(Y)$, respectively, and $E(X)$ is correct (see Definition 1.5(a)). In the present paper, we establish sufficient conditions under which the above statement remains valid for a densely defined linear continuous surjection $T: E_{p}(X) \\to E_{p}(Y)$. In particular, $\\mathcal{P}$ can be zero-dimensionality, $σ$-compactness or strong countable-dimensionality. Additionally, for arbitrary Tychonoff spaces $X$ and $Y$, assuming that $T: E_p(X)\\to E_p(Y)$ is a densely defined linear continuous operator, we show that $X\\in\\mathcal P$ implies $Y\\in\\mathcal P$, where $\\mathcal P$ is the property $(κ)$, the strong $σ$-scatteredness, or the property of being a $Δ_1$-space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37271",
  "author_total": 2,
  "authors": [
    {
      "name": "Arkady Leiderman"
    },
    {
      "name": "Vesko Valov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4tcmqgjd55gjt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37271",
  "fulltext_url": null,
  "id": "4tcmqgjd55gjt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37271",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7214959885",
  "pdf_url": "https://arxiv.org/pdf/2609.37271",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4tcmqgjd55gjt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37271",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37271"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On densely defined linear continuous operators between function spaces",
  "title_text": "On densely defined linear continuous operators between function spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/4tcmqgjd55gjt",
  "venue": "arXiv",
  "versions": []
}