Hilbert ProblemsTopological groups
Hilbert's Fifth Problem and the Hilbert–Smith Conjecture
Hilbert–Smith conjecture*: every locally compact topological group acting continuously and faithfully on a connected finite-dimensional topological manifold is a Lie group.
Mathematical statement
Hilbert–Smith conjecture*: every locally compact topological group acting continuously and faithfully on a connected finite-dimensional topological manifold is a Lie group.
Statement source: Hilbert Problems 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
hilbert_smith_conjecture
theorem hilbert_smith_conjecture [IsTopologicalGroup G] [LocallyCompactSpace G] [MulAction G X] [ContinuousSMul G X] [FaithfulSMul G X] : AdmitsLieGroupStructure G := 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