{
  "abstract": "In this paper, we study several properties concerning cut points and non-cut points. First, we show that the property of being a continuum consisting entirely of shore points is preserved under refinable maps. Next, we show that having a block point, having a non-shore point, and having a strong center point are not Whitney-reversible properties. Consequently, \\cite[Question 2.9]{nonweak} has a negative answer. Furthermore, we show that none of the classes of continua witnessing the failure of the sequential strong Whitney-reversible property for these three properties admits a common model. Finally, in connection with the fact that colocal connectedness is not a Whitney-reversible property, we show that the class of nonaposyndetic continua having a cut point and such that every positive Whitney level is colocally connected has no common model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31034",
  "author_total": 1,
  "authors": [
    {
      "name": "Eiichi Matsuhashi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a1g6ww1g2tk85.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31034",
  "fulltext_url": null,
  "id": "a1g6ww1g2tk85",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31034",
  "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|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7214616040",
  "pdf_url": "https://arxiv.org/pdf/2609.31034",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a1g6ww1g2tk85.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31034",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31034"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Whitney Properties and Whitney reversible properties of Cut and Non-Cut Points",
  "title_text": "Whitney Properties and Whitney reversible properties of Cut and Non-Cut Points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/a1g6ww1g2tk85",
  "venue": "arXiv",
  "versions": []
}