Conjectures about Weakly First Countable spaces
Problem 3 in [Ar2013]: Give an example in ZFC of a weakly first- countable compact Hausdorff space which is not first countable.
Mathematical statement
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.
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
existsWeaklyFirstCountableCompactNotFirstCountable
theorem existsWeaklyFirstCountableCompactNotFirstCountable : ∃ (X : Type) (_ : TopologicalSpace X), WeaklyFirstCountableTopology X ∧ CompactSpace X ∧ T2Space X ∧ ¬ FirstCountableTopology 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