Theorems · Theorem · category theory
CompHausLike.isClosedMap
∀ {P : TopCat → Prop} {X Y : CompHausLike P} (f : X ⟶ Y), IsClosedMap ⇑(CategoryTheory.ConcreteCategory.hom f)Any continuous function on compact Hausdorff spaces is a closed map.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setproof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- TopCatstatement and proof · cited by 1,889
- IsClosedproof · cited by 1,639
- CategoryTheory.InducedCategory.Hom.homproof · cited by 850
- CompHausLike.toTopstatement and proof · cited by 258
- TopCat.Hom.homproof · cited by 169
- CompHausLikestatement and proof · cited by 145
Cited by2
Results whose statement or proof uses this declaration.
- LightProfinite.isClosedMapproof · cited by 0
- CompHausLike.isIso_of_bijectiveproof · cited by 0