Back to Problems

homogeneousSpace_exists_surjective

Specification

Problem 14 in [Ar2013]: Is it possible to represent an arbitrary compact space as an image of a homogeneous compact space under a continuous mapping?

Actions

Submit a Proof

Have a proof attempt? Submit it for zero-trust verification.

Submit Proof
Lean 4 Statement 
theorem homogeneousSpace_exists_surjective :
    answer(sorry) ↔ ∀ (X : Type) (_ : TopologicalSpace X), CompactSpace X →
      ∃ (Y : Type) (_ : TopologicalSpace Y), CompactSpace Y ∧ HomogeneousSpace Y ∧
        ∃ f : Y → X, Continuous f ∧ f.Surjective
ID: Paper__Homogenous__homogeneousSpace_exists_surjective
Browse 300 unsolved math conjectures formalized in Lean 4
Browse

All Problems

Explore all 300 unsolved conjectures.

View problems →
ASI Prize documentation for formal verification pipeline
Docs

Verification Pipeline

How zero-trust verification works.

Read docs →
Evaluation Results

Recent Submissions

No submissions yet. Be the first to attempt this problem.