Conjectures around homogeneous topological spaces
Problem 13 in [Ar2013]: Is it true that every infinite homogeneous compact hausdorff space contains a non-trivial convergent sequence?
Mathematical statement
Problem 13 in [Ar2013]: Is it true that every infinite homogeneous compact hausdorff space contains a non-trivial convergent sequence?
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_inj_tendsto
theorem homogeneousSpace_exists_inj_tendsto : answer(sorry) ↔ ∀ (X : Type) (_ : TopologicalSpace X), ¬ Finite X → T2Space X → CompactSpace X → HomogeneousSpace X → ∃ s : ℕ → X, s.Injective ∧ ∃ a : X, Tendsto s atTop (nhds a) := 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