Theorems · Theorem · general topology
Topology.IsClosedEmbedding.t4Space
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [T4Space Y] {f : X → Y},
Topology.IsClosedEmbedding f → T4Space XIf the codomain of a closed embedding is a T₄ space, then so is the domain.
- Defined in
- Mathlib.Topology.Separation.Regular
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- T1Spaceproof · cited by 275
- Topology.IsClosedEmbeddingstatement and proof · cited by 195
- NormalSpaceproof · cited by 84
- Topology.IsClosedEmbedding.isEmbeddingproof · cited by 25
- T4Spacestatement and proof · cited by 12
- Topology.IsEmbedding.t1Spaceproof · cited by 3
- Topology.IsClosedEmbedding.normalSpaceproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Homeomorph.t4Spaceproof · cited by 1