{
  "abstract": "We introduce the notion of perfect regularity as an appropriate weakening of perfect normality, both for spaces and locales. Various characterizations are given, using Dedekind-MacNeille completions, injective hulls, and sublocales. We place the new class of perfectly regular frames among various well-studied classes of frames. We also introduce the construction of perfect regularization of a completely regular frame, compare it to Isbell's well-known booleanization construction, and argue that it is at least as important as the latter.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06990",
  "author_total": 3,
  "authors": [
    {
      "name": "Ana Belén Avilez"
    },
    {
      "name": "Guram Bezhanishvili"
    },
    {
      "name": "Joanne Walters-Wayland"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/55jgbkzscfg16.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06990",
  "fulltext_url": null,
  "id": "55jgbkzscfg16",
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  "landing_url": "https://arxiv.org/abs/2609.06990",
  "language": null,
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  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
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      "arxiv",
      "math.GN"
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      "arxiv",
      "math.RA"
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  "openalex": "W7212007862",
  "pdf_url": "https://arxiv.org/pdf/2609.06990",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/55jgbkzscfg16.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06990",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06990"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "An overlooked weakening of perfect normality: Perfect regularity in spaces and locales",
  "title_text": "An overlooked weakening of perfect normality: Perfect regularity in spaces and locales",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/55jgbkzscfg16",
  "venue": "arXiv",
  "versions": []
}