The Bing-Borsuk Conjecture
The Bing-Borsuk Conjecture: every -dimensional homogeneous absolute neighborhood retract is a topological -manifold. A topological space is an -dimensional manifold when T2Space X ∧ Nonempty (ChartedSpace (Fin n → ℝ) X). The hypothesis `[Metr...
Mathematical statement
The Bing-Borsuk Conjecture: every -dimensional homogeneous absolute neighborhood retract
is a topological -manifold. A topological space is an -dimensional manifold
when T2Space X ∧ Nonempty (ChartedSpace (Fin n → ℝ) X). The hypothesis [MetrizableSpace X]
implies T2Space X so this does not appear in the conclusion.
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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
bing_borsuk_conjecture
theorem bing_borsuk_conjecture : ∀ n : ℕ, ∀ (X : Type) [TopologicalSpace X] [MetrizableSpace X] [HomogeneousSpace X] [IsAbsoluteNeighborhoodRetract X], HasLebesgueCoveringDimensionEq X n → Nonempty (ChartedSpace (Fin n → ℝ) X) := 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