Theorems · Theorem · general topology
Compactum.continuous_of_hom
∀ {X Y : Compactum} (f : X ⟶ Y), Continuous ⇑(CategoryTheory.ConcreteCategory.hom f)Any morphism of compacta is continuous.
- Defined in
- Mathlib.Topology.Category.Compactum
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 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 and proof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- Filterproof · cited by 8,121
- nhdsproof · cited by 5,554
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- Continuousstatement · cited by 2,592
- Ultrafilterstatement and proof · cited by 193
- Ultrafilter.toFilterproof · cited by 172
- CategoryTheory.Monad.Algebra.Astatement and proof · cited by 81
- Ultrafilter.mapproof · cited by 26
- CategoryTheory.ofTypeMonadstatement · cited by 21
- Compactumstatement and proof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- compactumToCompHausproof · cited by 0