Conjectures around homogeneous topological spaces
Problem 16 in [Ar2013]: Is the cardinality of every homogeneous ฯ-monolithic compact hausdorff space not greater than ๐ ?
Mathematical statement
Problem 16 in [Ar2013]: Is the cardinality of every homogeneous ฯ-monolithic compact hausdorff space not greater than ๐ ?
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_card_lt
theorem countablyMonolithicSpace_card_lt : answer(sorry) โ โ (X : Type) (_ : TopologicalSpace X), T2Space X โ CompactSpace X โ HomogeneousSpace X โ CountablyMonolithicSpace X โ #X โค ๐ := 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