{
  "abstract": "Let $L/K$ be an arbitrary Galois extension with group $G$, equipped with the Krull topology. Let $C(G,K)$ denote the $K$-vector space of continuous functions $G\\to K$, with $K$ discrete and $G$ acting by left translation. We prove that there exists a $G$-equivariant $K$-linear isomorphism $φ:C(G,K)\\to L$ such that, for every open subgroup $H$ of $G$, the map $φ^H:C(H,L^H)\\to L$ induced by extension by zero and extension of scalars is an $H$-equivariant $L^H$-linear isomorphism. This gives a completely normal analogue of Lenstra's infinite normal basis theorem; the case of finite base fields was previously established in an equivalent form by Hachenberger.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22247",
  "author_total": 1,
  "authors": [
    {
      "name": "Patrik Lundström"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2p1nzjfx477tf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22247",
  "fulltext_url": null,
  "id": "2p1nzjfx477tf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22247",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.22247",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2p1nzjfx477tf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22247",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22247"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An infinite completely normal basis theorem",
  "title_text": "An infinite completely normal basis theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/2p1nzjfx477tf",
  "venue": "arXiv",
  "versions": []
}