toEquiv_injective — Mathlib

English

Two homeomorphisms are equal if their underlying equivalences are equal.

Русский

Две гомоморфистики равны, если их лежащие под ними эквивалентности равны.

LaTeX

$$$$ \mathrm{Injective}(\mathrm{toEquiv}): \forall X Y\; [\text{TopologicalSpace } X] [\text{TopologicalSpace } Y],\; \text{Injective}(\mathrm{toEquiv}: X\equiv_t Y \to X\equiv Y). $$$$

Lean4

theorem toEquiv_injective : Function.Injective (toEquiv : X ≃ₜ Y → X ≃ Y)
  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl

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