{
  "abstract": "In the context of constructive reverse mathematics, we show that Brouwer's fixed-point theorem and weak König's lemma (WKL) are equivalent. To derive WKL from Brouwer's fixed-point theorem, the construction of a continuous function on the unit square without fixed points due to Orevkov [Soviet Math. Doklady (1963), 1253--1256] is generalised to yield a uniformly continuous function on the unit square whose fixed points encode information about infinite paths of a given infinite tree.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04644",
  "author_total": 1,
  "authors": [
    {
      "name": "Tatsuji Kawai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7mbx77s0dnbev.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04644",
  "fulltext_url": null,
  "id": "7mbx77s0dnbev",
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  "landing_url": "https://arxiv.org/abs/2609.04644",
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  "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.LO"
    ],
    [
      "openalex",
      "1703|Computability, Logic, AI Algorithms"
    ]
  ],
  "openalex": "W7211900068",
  "pdf_url": "https://arxiv.org/pdf/2609.04644",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7mbx77s0dnbev.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2609.04644",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04644"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Constructive equivalence between Brouwer's fixed-point theorem and weak König's lemma",
  "title_text": "Constructive equivalence between Brouwer's fixed-point theorem and weak König's lemma",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/7mbx77s0dnbev",
  "venue": "arXiv",
  "versions": []
}