Hilbert ProblemsTopological groups
Hilbert's Fifth Problem and the Hilbert–Smith Conjecture
Equivalent p-adic formulation: the p-adic integers ℤ_[p] cannot act continuously and faithfully on any connected finite-dimensional topological manifold. By the Gleason–Yamabe theorem, this is equivalent to hilbert_smith_conjecture.
Mathematical statement
Equivalent p-adic formulation: the p-adic integers ℤ_[p] cannot act continuously and
faithfully on any connected finite-dimensional topological manifold. By the Gleason–Yamabe
theorem, this is equivalent to hilbert_smith_conjecture.
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_padic_formulation
theorem hilbert_smith_padic_formulation (p : ℕ) [Fact p.Prime] [AddAction (PadicInt p) X] [ContinuousVAdd (PadicInt p) X] [FaithfulVAdd (PadicInt p) X] : False := 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