Pith Number

pith:OV7EM5LV

pith:2026:OV7EM5LVHM7QEZENNJ6VRMMF2U

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The Baire property in uniform spaces: a survey

\'Alvaro Garc\'ia Zambrano, Fernando Rambla Barreno, Francisco Javier Garc\'ia Pacheco

Complete uniform spaces do not automatically satisfy the Baire property unlike complete pseudometric spaces.

arxiv:2605.18225 v1 · 2026-05-18 · math.GN

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We decide to explore some conditions, such as countable compactness, pseudocompactness and pseudocompleteness, and see in which circumstances a general complete uniform space satisfies the Baire property.

C2weakest assumption

The premise that the Baire property does not hold automatically for complete uniform spaces (unlike the pseudometric case) and that the listed conditions are the relevant ones to check; this enters in the abstract's contrast between metric and uniform settings.

C3one line summary

The paper surveys conditions such as countable compactness, pseudocompactness, and pseudocompleteness for when complete uniform spaces satisfy the Baire property.

References

11 extracted · 11 resolved · 0 Pith anchors

[1] I. M. James,Introduction to Uniform Spaces, Fields Institute Monographs, Springer New York, 2012 2012

[2] Willard,General Topology, Courier Corporation, 2004 2004

[3] J. L. Kelley,General Topology, Springer, New York, 1955 1955

[4] Engelking,General Topology, Sigma Series in Pure Mathematics, Vol 1989

[5] Quasiregular, pseudocomplete, and Baire spaces 1981

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:05:51.264377Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

757e4675753b3f02648d6a7d58b185d5217c18d829e009afb6cfb7462c78463c

Aliases

arxiv: 2605.18225 · arxiv_version: 2605.18225v1 · doi: 10.48550/arxiv.2605.18225 · pith_short_12: OV7EM5LVHM7Q · pith_short_16: OV7EM5LVHM7QEZEN · pith_short_8: OV7EM5LV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OV7EM5LVHM7QEZENNJ6VRMMF2U \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 757e4675753b3f02648d6a7d58b185d5217c18d829e009afb6cfb7462c78463c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e077de6029f50be24808ffffbae67cab845ea878e86ff8c65c7c31e6cfce817a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2026-05-18T11:10:42Z",
    "title_canon_sha256": "773ddddef2a65e0ac060966b75ab6c16f1ef650d0014e90e5a8f37c2245774df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18225",
    "kind": "arxiv",
    "version": 1
  }
}