Theorems · Theorem · algebraic geometry

AlgebraicGeometry.isOpenImmersion_eq_inf

AlgebraicGeometry.IsOpenImmersion =
  (AlgebraicGeometry.topologically fun {α β} [TopologicalSpace α] [TopologicalSpace β] => Topology.IsOpenEmbedding) ⊓
    AlgebraicGeometry.stalkwise fun {R S} [CommRing R] [CommRing S] x => Function.Bijective ⇑x

Defined in: Mathlib.AlgebraicGeometry.Morphisms.OpenImmersion
Cited by: 1 results in Mathlib
Foundations: Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites21

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.Homproof · cited by 32,603
TopologicalSpacestatement and proof · cited by 24,529
CommRingstatement and proof · cited by 17,173
RingHomstatement and proof · cited by 10,189
TopCat.carrierproof · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CategoryTheory.MorphismPropertystatement · cited by 2,179
AlgebraicGeometry.PresheafedSpace.carrierproof · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.isomorphisms_eq_stalkwiseproof · cited by 0