Source labels openChecked July 26, 2026

Conjectures about Weakly First Countable spaces

Problem 2 in [Ar2013]: Give an example in ZFC of a weakly first- countable compact Hausdorff space X such that $𝔠 < |X|$ .

General topology AMS 54

Mathematical statement

Problem 2 in [Ar2013]: Give an example in ZFC of a weakly first- countable compact Hausdorff space X such that $𝔠 < |X|$ .

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

Statement source: Papers statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

existsWeaklyFirstCountableCompactBig

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem existsWeaklyFirstCountableCompactBig : answer(sorry) ↔    ∃ (X : Type) (_ : TopologicalSpace X),      WeaklyFirstCountableTopology X ∧ CompactSpace X ∧ T2Space X ∧        𝔠 < #X := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization