Theorems · Definition · algebraic geometry
CategoryTheory.Iso.schemeIsoToHomeo
{X Y : AlgebraicGeometry.Scheme} → (X ≅ Y) → ↥X ≃ₜ ↥YAlias of AlgebraicGeometry.Scheme.homeoOfIso.
An isomorphism of schemes induces a homeomorphism of the underlying topological spaces.
- Defined in
- Mathlib.AlgebraicGeometry.Scheme
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Isostatement · cited by 3,963
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- Homeomorphstatement · cited by 725
- AlgebraicGeometry.Scheme.homeoOfIsoproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.homeomorphproof · cited by 13