prodMap — Mathlib

English

If f and g are homeomorphisms, then their product map on a binary product is a homeomorphism.

Русский

Если f и g — гомеоморфизмы, entonces их произведение на двойном произведении — гомеоморфизм.

LaTeX

$$$\IsHomeomorph f \to \IsHomeomorph g \to IsHomeomorph(\mathrm{Prod.map}(f,g))$$$

Lean4

theorem prodMap {g : Z → W} (hf : IsHomeomorph f) (hg : IsHomeomorph g) : IsHomeomorph (Prod.map f g) :=
  ⟨hf.1.prodMap hg.1, hf.2.prodMap hg.2, hf.3.prodMap hg.3⟩

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