Theorems · Theorem · algebraic geometry
AlgebraicGeometry.quasiCompact_iff_compactSpace
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [QuasiSeparatedSpace ↥Y] [CompactSpace ↥Y],
AlgebraicGeometry.QuasiCompact f ↔ CompactSpace ↥X- Cited by
- 2 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- 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
- CompactSpacestatement and proof · cited by 593
- AlgebraicGeometry.QuasiCompactstatement and proof · cited by 102
- QuasiSeparatedSpacestatement and proof · cited by 49
- AlgebraicGeometry.QuasiCompact.compactSpace_of_compactSpaceproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsZariskiLocalAtTarget.descendsAlong_inf_quasiCompactproof · cited by 2
- AlgebraicGeometry.isIntegral_appTop_of_universallyClosedproof · cited by 1