Theorems · Theorem · general topology
Topology.IsClosedEmbedding.normalSpace
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [NormalSpace Y] {f : X → Y},
Topology.IsClosedEmbedding f → NormalSpace XIf the codomain of a closed embedding is a normal space, then so is the domain.
- Defined in
- Mathlib.Topology.Separation.Regular
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Disjointproof · cited by 2,201
- IsClosedproof · cited by 1,639
- Topology.IsClosedEmbeddingstatement and proof · cited by 195
- Topology.IsEmbedding.injectiveproof · cited by 103
- NormalSpacestatement and proof · cited by 84
- Set.subset_preimage_imageproof · cited by 44
- SeparatedNhdsproof · cited by 33
- Topology.IsClosedEmbedding.toIsEmbeddingproof · cited by 27
- Topology.IsClosedEmbedding.continuousproof · cited by 25
Cited by2
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.t4Spaceproof · cited by 1
- Homeomorph.normalSpaceproof · cited by 0