Conjectures around homogeneous topological spaces
Problem 14 in [Ar2013]: Is it possible to represent an arbitrary compact hausdorff space as an image of a homogeneous compact space under a continuous mapping?
Mathematical statement
Problem 14 in [Ar2013]: Is it possible to represent an arbitrary compact hausdorff space as an image of a homogeneous compact space under a continuous mapping?
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
homogeneousSpace_exists_surjective
theorem homogeneousSpace_exists_surjective : answer(sorry) ↔ ∀ (X : Type) (_ : TopologicalSpace X), T2Space X → CompactSpace X → ∃ (Y : Type) (_ : TopologicalSpace Y), T2Space Y ∧ CompactSpace Y ∧ HomogeneousSpace Y ∧ ∃ f : Y → X, Continuous f ∧ f.Surjective := 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