Conjectures around homogeneous topological spaces
Problem 17 in [Ar2013]: Is it true that every nonempty ω-monolithic compact hausdorff space contains a point with a first countable neighborhood basis?
Mathematical statement
Problem 17 in [Ar2013]: Is it true that every nonempty ω-monolithic compact hausdorff space contains a point with a first countable neighborhood basis?
Note: Nonempty X is required since the conclusion asserts the existence of a point.
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
countablyMonolithicSpace_exists_nhds_generated_countable
theorem countablyMonolithicSpace_exists_nhds_generated_countable : answer(sorry) ↔ ∀ (X : Type) (_ : TopologicalSpace X), T2Space X → CompactSpace X → Nonempty X → CountablyMonolithicSpace X → ∃ x : X, (𝓝 x).IsCountablyGenerated := 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