{
  "id": "2301.12748",
  "version": "v1",
  "published": "2023-01-30T09:26:36.000Z",
  "updated": "2023-01-30T09:26:36.000Z",
  "title": "Resolvability and complete accumulation points",
  "authors": [
    "A. E. Lipin"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We prove that: I. For every regular Lindel\\\"of space $X$ if $|X|=\\Delta(X)$ and $\\mathrm{cf}|X|\\ne\\omega$, then $X$ is maximally resolvable; II. For every regular countably compact space $X$ if $|X|=\\Delta(X)$ and $\\mathrm{cf}|X|=\\omega$, then $X$ is maximally resolvable. Here $\\Delta(X)$, the dispersion character of $X$, is the minimum cardinality of a nonempty open subset of $X$. Statements I and II are corollaries of the main result: for every regular space $X$ if $|X|=\\Delta(X)$ and every set $A\\subseteq X$ of cardinality $\\mathrm{cf}|X|$ has a complete accumulation point, then $X$ is maximally resolvable. Moreover, regularity here can be weakened to $\\pi$-regularity, and the Lindel\\\"of property can be weakened to the linear Lindel\\\"of property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-30T09:26:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete accumulation point",
      "resolvability",
      "maximally resolvable",
      "nonempty open subset",
      "regular countably compact space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}