toHomeomorph — Mathlib

English

Any diffeomorphism induces a homeomorphism between its domain and codomain.

Русский

Любой диффеоморфизм индуцирует гомеоморфизм между своей областью определения и кодом.

LaTeX

$$$\\text{If } h: M \\to N \\text{ is a diffeomorphism, then } h \\text{ is a homeomorphism.}$$$

Lean4

/-- A diffeomorphism is a homeomorphism. -/
def toHomeomorph (h : M ≃ₘ^n⟮I, J⟯ N) : M ≃ₜ N :=
  ⟨h.toEquiv, h.continuous, h.symm.continuous⟩

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