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mathoverflow_235893

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Does there exist a bijection $f : ℝ^n → ℝ^n$ such that $f$ is connected but the inverse is not?

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Lean 4 Statement 
theorem mathoverflow_235893 :
    answer(sorry) ↔ ∀ n > 0, ∃ (f : ℝ^n ≃ ℝ^n), IsConnectedMap f ∧ ¬ IsConnectedMap f.symm
ID: Mathoverflow__235893__mathoverflow_235893
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