{
  "abstract": "On a totally bounded metric space every non-contractive self-map is an isometry. For quasi-metric spaces, taken T_1 throughout, this fails: Zavarzina gave a hereditarily precompact counterexample and asked whether bijectivity restores rigidity; the toll spiral shows that it does not. We prove that compactness does: every compact quasi-metric space is expand-contract plastic, that is, each of its bijective non-contractive self-maps is an isometry. Countable compactness suffices, as does compactness of the conjugate topology. Bijectivity cannot be dropped: a compact, hereditarily precompact quasi-metric on the natural numbers makes the shift non-contractive and not an isometry. For arbitrary non-contractive self-maps we prove rigidity when the space is hereditarily precompact and its conjugate topology is sequentially compact, in particular when it is hereditarily precompact and Yoneda complete; neither hypothesis can be dropped. In both theorems the T_1 axiom can be weakened to R_0, with hereditary precompactness read sequentially, but not to T_0: we construct a T_0 space with all the remaining hypotheses of both theorems, carrying a bijective non-contractive self-map that is not an isometry. Under R_0 the two-sided case reduces to the metric theorem; the one-sided theorems do not, and plasticity does not pass to the symmetrization even for compact spaces. In finite dimension the unit ball of a T_1 asymmetric normed space, forward or symmetric, and its sphere are rigid for every non-contractive self-map; without T_1 the forward ball need not be; in infinite dimension the symmetric ball and sphere are not plastic in general, and the forward versions carry the quasi-metric form of the unit-ball question of Cascales, Kadets, Orihuela and Wingler, which is posed. The two theorems are machine-checked in Lean, and so are the counterexamples, apart from a few statements listed at the end.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14301",
  "author_total": 1,
  "authors": [
    {
      "name": "Thomas Duzer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/52z1f6xnjhmff.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14301",
  "fulltext_url": null,
  "id": "52z1f6xnjhmff",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14301",
  "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.FA"
    ],
    [
      "openalex",
      "2608|Fixed Point Theorems Analysis"
    ]
  ],
  "openalex": "W7221835499",
  "pdf_url": "https://arxiv.org/pdf/2610.14301",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/52z1f6xnjhmff.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.14301",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14301"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Compact Quasi-Metric Spaces Are Expand-Contract Plastic",
  "title_text": "Compact Quasi-Metric Spaces Are Expand-Contract Plastic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/52z1f6xnjhmff",
  "venue": "arXiv",
  "versions": []
}