Theorems · Theorem · general topology
JacobsonSpace.of_isOpenEmbedding
∀ {X : Type u_2} {Y : Type u_1} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} [JacobsonSpace Y],
Topology.IsOpenEmbedding f → JacobsonSpace X- Defined in
- Mathlib.Topology.JacobsonSpace
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.imageproof · cited by 5,609
- Set.Nonemptyproof · cited by 2,627
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- Set.Nonempty.imageproof · cited by 87
- IsLocallyClosedproof · cited by 44
- Topology.IsOpenEmbedding.isOpen_rangeproof · cited by 33
- closedPointsproof · cited by 25
- IsOpen.isLocallyClosedproof · cited by 20
- JacobsonSpacestatement and proof · cited by 20
- Topology.IsOpenEmbedding.isInducingproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.LocallyOfFiniteType.jacobsonSpaceproof · cited by 2
- TopologicalSpace.IsOpenCover.jacobsonSpace_iffproof · cited by 1
- AlgebraicGeometry.isFinite_iff_locallyOfFiniteType_of_jacobsonSpaceproof · cited by 1