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Source labels openChecked July 26, 2026

PapersGeneral topology

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

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem countablyMonolithicSpace_card_lt :    answer(sorry) โ†” โˆ€ (X : Type) (_ : TopologicalSpace X), T2Space X โ†’ CompactSpace X โ†’      HomogeneousSpace X โ†’ CountablyMonolithicSpace X โ†’ #X โ‰ค 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