Theorems · Theorem · algebraic geometry
AlgebraicGeometry.compactSpace_iff_exists
∀ {X : AlgebraicGeometry.Scheme}, CompactSpace ↥X ↔ ∃ R f, Function.Surjective ⇑f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
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
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Top.topproof · cited by 9,680
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement and proof · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isClosedMap_iff_specializingMapproof · cited by 1
- AlgebraicGeometry.isCompact_iff_existsproof · cited by 0