{
  "id": "2308.01259",
  "version": "v1",
  "published": "2023-08-02T16:29:35.000Z",
  "updated": "2023-08-02T16:29:35.000Z",
  "title": "On resolvability, connectedness and pseudocompactness",
  "authors": [
    "Anton Lipin"
  ],
  "comment": "12 pages, no figures",
  "categories": [
    "math.GN"
  ],
  "abstract": "We prove that: I. If $L$ is a $T_1$ space, $|L|>1$ and $d(L) \\leq \\kappa \\geq \\omega$, then there is a submaximal dense subspace $X$ of $L^{2^\\kappa}$ such that $|X|=\\Delta(X)=\\kappa$; II. If $\\frak{c}\\leq\\kappa=\\kappa^\\omega<\\lambda$ and $2^\\kappa=2^\\lambda$, then there is a Tychonoff pseudocompact globally and locally connected space $X$ such that $|X|=\\Delta(X)=\\lambda$ and $X$ is not $\\kappa^+$-resolvable; III. If $\\omega_1\\leq\\kappa<\\lambda$ and $2^\\kappa=2^\\lambda$, then there is a regular space $X$ such that $|X|=\\Delta(X)=\\lambda$, all continuous real-valued functions on $X$ are constant (so $X$ is pseudocompact and connected) and $X$ is not $\\kappa^+$-resolvable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-02T16:29:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "resolvability",
      "pseudocompactness",
      "connectedness",
      "submaximal dense subspace",
      "tychonoff pseudocompact"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}