therefore
Sign up
Open navigation
All open problems
Source labels openChecked July 26, 2026

MathOverflowReal functions

Mathoverflow 235893

Assume for n>1n>1, f:Rn→Rnf:\mathbb{R}^n\to\mathbb{R}^n is a bijection, where Rn\mathbb{R}^n is equipped with the standard topology. Does the connectedness of (the induced power set map) ff imply that of f−1f^{-1}?

Real functionsAMS 26AMS 54

Mathematical statement

Assume for n>1n>1, f:Rn→Rnf:\mathbb{R}^n\to\mathbb{R}^n is a bijection, where Rn\mathbb{R}^n is equipped with the standard topology. Does the connectedness of (the induced power set map) ff imply that of f−1f^{-1}?

Statement source: MathOverflow statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

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

mathoverflow_235893

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem mathoverflow_235893 :    answer(sorry) ↔ ∀ n > 1, ∀ (f : ℝ^n ≃ ℝ^n), IsConnectedMap f → IsConnectedMap f.symm := 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

Pinned Formal Conjectures sourceformalizationmathoverflow/235893background*Willie Wong*background