Open Research Index

Hilbert–Smith and p-adic exclusion with second countability

adbrw

Palomar Registrypalomar/PALOMAR-2026-10-16-000006Oct 16, 2026math.GTscore 0

A Lean formalization of the Hilbert–Smith statement for a second-countable locally compact Hausdorff topological group acting continuously and faithfully on a connected, Hausdorff, second-countable, finite-dimensional topological manifold. The conclusion gives a smooth real Lie-group structure for the group's existing topology. The development also proves p-adic exclusion for second-countable manifolds and provides universe-polymorphic versions. No second-countability hypothesis is dropped.

SourceRepositoryJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/palomar/PALOMAR-2026-10-16-000006
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-16-000006/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-16-000006/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'