Theorems · Theorem · general topology
Topology.IsClosedEmbedding.of_continuous_injective_isClosedMap
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
Continuous f → Function.Injective f → IsClosedMap f → Topology.IsClosedEmbedding f- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Compl.complproof · cited by 2,925
- Continuousstatement and proof · cited by 2,592
- IsOpenproof · cited by 2,400
- LE.le.antisymmproof · cited by 507
- compl_complproof · cited by 229
- Topology.IsClosedEmbeddingstatement · cited by 195
- IsClosedMapstatement and proof · cited by 138
- IsClosed.isOpen_complproof · cited by 126
- Set.preimage_image_eqproof · cited by 87
Cited by7
Results whose statement or proof uses this declaration.
- Continuous.isClosedEmbeddingproof · cited by 5
- Topology.IsClosedEmbedding.sigmaMkproof · cited by 3
- isClosedEmbedding_updateproof · cited by 1
- isSeparatedMap_iff_isClosedMapproof · cited by 0
- AlgebraicGeometry.IsClosedImmersion.of_comp_isClosedImmersionproof · cited by 0
- LightProfinite.isClosedEmbedding_natUnionInftyEmbeddingproof · cited by 0