Theorems · Inductive type · general topology
CompletelyNormalSpace
(X : Type u) → [TopologicalSpace X] → Prop
A topological space X is a completely normal space provided that for any two sets s, t
such that if both closure s is disjoint with t, and s is disjoint with closure t,
then there exist disjoint neighbourhoods of s and t.
- Defined in
- Mathlib.Topology.Separation.Regular
- Cited by
- 9 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 by13
Results whose statement or proof uses this declaration.
- completelyNormalSpace_iff_forall_isOpen_normalSpacestatement and proof · cited by 3
- t5Space_iff_forall_isOpen_t4Spaceproof · cited by 2
- Topology.IsEmbedding.t5Spaceproof · cited by 1
- CompletelyNormalSpace.completely_normalstatement and proof · cited by 1
- Topology.IsInducing.completelyNormalSpacestatement and proof · cited by 1
- completelyNormalSpace_iff_forall_normalSpacestatement and proof · cited by 1
- UniformSpace.completelyNormalSpace_of_hasAntitoneBasisstatement · cited by 0
- T5Space.casesOnstatement and proof · cited by 0
- T5Space.recOnstatement and proof · cited by 0
- CompletelyNormalSpace.casesOnstatement and proof · cited by 0
- CompletelyNormalSpace.of_forall_isOpen_normalSpacestatement · cited by 0
- CompletelyNormalSpace.of_forall_normalSpacestatement · cited by 0