Theorems · Theorem · category theory
CompHausLike.isIso_of_bijective
∀ {P : TopCat → Prop} {X Y : CompHausLike P} (f : X ⟶ Y),
Function.Bijective ⇑(CategoryTheory.ConcreteCategory.hom f) → CategoryTheory.IsIso fAny continuous bijection of compact Hausdorff spaces is an isomorphism.
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- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Setproof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- Equivproof · cited by 8,337
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- Equiv.symmproof · cited by 3,681
- TopCat.carrierstatement and proof · cited by 3,184
- Continuousproof · cited by 2,592
- ContinuousMapstatement · cited by 2,491
- TopCatstatement and proof · cited by 1,889
- IsClosedproof · cited by 1,639
- CategoryTheory.IsIsostatement · cited by 1,156
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