{
  "abstract": "In this survey, we review certain types of special \\(T_{1}\\) spaces and their associated fixed-point theorems. Kupka introduced the notion of a feeble topological contraction, which naturally generalizes Lipschitz contractions defined on metric spaces. Specifically, Kupka established a fixed-point theorem for feeble topological contractions possessing a closed graph within the product of arbitrary \\(T_{0}\\) spaces. Furthermore, the \\(T_{1}\\) separation axiom is shown to guaranty the uniqueness of such fixed points. Finally, we discuss peripheral Hausdorff and locally Hausdorff spaces within the context of these fixed-point results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20602",
  "author_total": 1,
  "authors": [
    {
      "name": "Robert Rałowski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1mz83ezfs2m9d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20602",
  "fulltext_url": null,
  "id": "1mz83ezfs2m9d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20602",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GN"
    ],
    [
      "openalex",
      "2608|Fixed Point Theorems Analysis"
    ]
  ],
  "openalex": "W7213594746",
  "pdf_url": "https://arxiv.org/pdf/2609.20602",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1mz83ezfs2m9d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20602",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20602"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Journey into special $T_1$-spaces",
  "title_text": "Journey into special T_1-spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/1mz83ezfs2m9d",
  "venue": "arXiv",
  "versions": []
}