Theorems · Theorem · general topology
normal_separation
∀ {X : Type u_1} [inst : TopologicalSpace X] [NormalSpace X] {s t : Set X},
IsClosed s → IsClosed t → Disjoint s t → SeparatedNhds s t- Defined in
- Mathlib.Topology.Separation.Regular
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceNormalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Disjointstatement and proof · cited by 2,201
- IsClosedstatement and proof · cited by 1,639
- NormalSpacestatement and proof · cited by 84
- SeparatedNhdsstatement · cited by 33
- NormalSpace.normalproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- normal_exists_closure_subsetproof · cited by 5
- completelyNormalSpace_iff_forall_isOpen_normalSpaceproof · cited by 3
- connectedComponent_eq_iInter_isClopenproof · cited by 2
- IsClosed.two_pow_mk_le_two_pow_mk_denseproof · cited by 2
- disjoint_nhdsSet_nhdsSetproof · cited by 0