Theorems · Inductive type · general topology
NormalSpace
(X : Type u) → [TopologicalSpace X] → Prop
A topological space is said to be a normal space if any two disjoint closed sets have disjoint open neighborhoods.
- Defined in
- Mathlib.Topology.Separation.Regular
- Cited by
- 84 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 by92
Results whose statement or proof uses this declaration.
- exists_continuous_zero_one_of_isClosedstatement and proof · cited by 10
- normal_exists_closure_subsetstatement and proof · cited by 5
- normal_separationstatement and proof · cited by 5
- exists_subset_iUnion_closed_subsetstatement and proof · cited by 4
- exists_subset_iUnion_closure_subsetstatement and proof · cited by 3
- completelyNormalSpace_iff_forall_isOpen_normalSpacestatement and proof · cited by 3
- MeasureTheory.MemLp.exists_boundedContinuous_eLpNorm_sub_lestatement and proof · cited by 3
- MeasureTheory.MemLp.exists_hasCompactSupport_eLpNorm_sub_lestatement and proof · cited by 3
- ContinuousMap.exists_restrict_eqstatement and proof · cited by 3
- MeasureTheory.Lp.boundedContinuousFunction_densestatement and proof · cited by 2
- MeasureTheory.exists_continuous_eLpNorm_sub_le_of_closedstatement and proof · cited by 2
- Topology.IsInducing.perfectlyNormalSpaceproof · cited by 2