Theorems · Definition · category theory
TopologicalSpace.Opens.inclusionTopIso
(X : TopCat) → (TopologicalSpace.Opens.toTopCat X).obj ⊤ ≅ X
The inclusion of the top open subset (i.e. the whole space) is an isomorphism.
- Defined in
- Mathlib.Topology.Category.TopCat.Opens
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement · cited by 19,642
- Top.topstatement and proof · cited by 9,680
- CategoryTheory.Isostatement · cited by 3,963
- TopCat.carrierstatement and proof · cited by 3,184
- TopologicalSpace.Opensstatement · cited by 2,040
- TopCatstatement and proof · cited by 1,889
- TopologicalSpace.Opens.toTopCatstatement · cited by 81
- TopologicalSpace.Opens.inclusion'proof · cited by 73
- TopCat.ofHomproof · cited by 44
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.PresheafedSpace.toRestrictTopproof · cited by 4
- TopologicalSpace.Opens.inclusion'_top_functorstatement and proof · cited by 1
- AlgebraicGeometry.PresheafedSpace.restrict_top_presheafstatement and proof · cited by 1
- AlgebraicGeometry.PresheafedSpace.toRestrictTop_basestatement · cited by 0
- AlgebraicGeometry.PresheafedSpace.toRestrictTop_cstatement · cited by 0