Conjectures about Weakly First Countable spaces

formal-conjectures · paper · ams-54

This file formalizes the notion of a weakly first countable topological space and some conjectures
around those.

Problem 3 in [Ar2013]: Give an example in ZFC of a weakly first-
countable compact Hausdorff space which is not first countable.

Note: [Ar2013] uses a blanket convention that all spaces are
Tychonoff and "compact" means compact Hausdorff.

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://www.math.md/files/basm/y2013-n2-3/y2013-n2-3-
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://www.mathnet.ru/links/016f74007f9f96fa3aadae05cbd98457/dan40570.pdf
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Paper/WeaklyFirstCountable.lean
Local target: Corpus.PaperWeaklyFirstCountable.existsWeaklyFirstCountableCompactNotFirstCountable
Source SHA-256: d474a122ae0021309b637ae0e9b3e22ee64c1c44b84bce3d509f3074618cedec
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record