Theorems · Theorem · algebraic geometry
AlgebraicGeometry.QuasiCompact.compactSpace_of_compactSpace
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.QuasiCompact f] [CompactSpace ↥Y], CompactSpace ↥X- Cited by
- 7 results in Mathlib
- Foundations
- Depth 101 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.
- Setproof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- Set.univproof · cited by 3,945
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- IsCompactproof · cited by 1,282
- CompactSpacestatement and proof · cited by 593
Cited by7
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IsQuasiAffine.of_isAffineHomproof · cited by 2
- AlgebraicGeometry.quasiCompact_iff_compactSpaceproof · cited by 2
- AlgebraicGeometry.Scheme.compactSpace_of_isLimitproof · cited by 2
- AlgebraicGeometry.Flat.isQuotientMap_of_surjectiveproof · cited by 1
- AlgebraicGeometry.Scheme.isPullback_toSpecΓ_toSpecΓproof · cited by 1
- AlgebraicGeometry.isClosedMap_iff_specializingMapproof · cited by 1
- AlgebraicGeometry.IsFinite.of_locallyQuasiFiniteproof · cited by 0