Theorems · Inductive type · general topology
PerfectlyNormalSpace
(X : Type u) → [TopologicalSpace X] → Prop
A topological space X is a perfectly normal space provided it is normal and
closed sets are Gδ.
- Defined in
- Mathlib.Topology.Separation.GDelta
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by10
Results whose statement or proof uses this declaration.
- IsClosed.isGδstatement and proof · cited by 2
- Topology.IsInducing.perfectlyNormalSpacestatement and proof · cited by 2
- PerfectlyNormalSpace.closed_gdeltastatement and proof · cited by 1
- T6Space.casesOnstatement and proof · cited by 0
- PerfectlyNormalSpace.recOnstatement and proof · cited by 0
- T6Space.recOnstatement and proof · cited by 0
- Topology.IsEmbedding.t6Spaceproof · cited by 0
- Topology.IsEmbedding.perfectlyNormalSpacestatement · cited by 0
- perfectlyNormalSpace_iff_forall_isClosed_preimage_zerostatement and proof · cited by 0
- PerfectlyNormalSpace.casesOnstatement and proof · cited by 0