Open Research Index

Open Baire-space representation of Polish spaces

Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

Palomar Registrypalomar/PALOMAR-2026-10-22-000041Oct 22, 2026math.GNscore 0

Every nonempty Polish space is the image of Baire space, the product of countably many discrete natural-number spaces, under a continuous open surjection. The proof constructs a countably branching nonempty open scheme with nested closures, covering children and geometrically shrinking diameters. The image of each basic cylinder is proved exactly equal to its scheme open set. This yields openness and surjectivity of the limit map; existence is also characterized by nonemptiness. These are classical results, with no novelty or priority claim.

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-2026-10-22-000041
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-22-000041/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-22-000041/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'