Mathlib Map

Theorems · Theorem · algebraic geometry

AlgebraicGeometry.QuasiCompact.compactSpace_of_compactSpace

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.QuasiCompact f] [CompactSpace ↥Y], CompactSpace ↥X
Defined in
Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact
Cited by
7 results in Mathlib
Foundations
Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.QuasiCompactCompactSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.Scheme.IsQuasiAffine.of_isAffineHom · cited by 2IsQuasiAffine.of_isAffine…AlgebraicGeometry.quasiCompact_iff_compactSpace · cited by 2AlgebraicGeometry.quasiCo…AlgebraicGeometry.Scheme.compactSpace_of_isLimit · cited by 2Scheme.compactSpace_of_is…AlgebraicGeometry.Flat.isQuotientMap_of_surjective · cited by 1Flat.isQuotientMap_of_sur…AlgebraicGeometry.Scheme.isPullback_toSpecΓ_toSpecΓ · cited by 1Scheme.isPullback_toSpecΓ…AlgebraicGeometry.isClosedMap_iff_specializingMap · cited by 1AlgebraicGeometry.isClose…AlgebraicGeometry.IsFinite.of_locallyQuasiFinite · cited by 0IsFinite.of_locallyQuasiF…Set · cited by 53352SetQuiver.Hom · cited by 32603Quiver.HomSet.univ · cited by 3945Set.univTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…IsCompact · cited by 1282IsCompactCompactSpace · cited by 593CompactSpaceisOpen_univ · cited by 112isOpen_univAlgebraicGeometry.QuasiCompact · cited by 102AlgebraicGeometry.QuasiCo…Set.preimage_univ · cited by 46Set.preimage_univQuasiCompact.compactSpace_of_…CITED BYCITES

Cites17

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by7

Results whose statement or proof uses this declaration.