Theorems · Theorem · general topology
normal_exists_closure_subset
∀ {X : Type u_1} [inst : TopologicalSpace X] [NormalSpace X] {s t : Set X},
IsClosed s → IsOpen t → s ⊆ t → ∃ u, IsOpen u ∧ s ⊆ u ∧ closure u ⊆ t- Defined in
- Mathlib.Topology.Separation.Regular
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 63 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.
Cites15
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
- Compl.complproof · cited by 2,925
- IsOpenstatement and proof · cited by 2,400
- Disjointproof · cited by 2,201
- IsClosedstatement and proof · cited by 1,639
- closurestatement · cited by 1,254
- Set.Subset.transproof · cited by 218
- Set.disjoint_leftproof · cited by 121
- closure_minimalproof · cited by 94
- NormalSpacestatement and proof · cited by 84
- Disjoint.le_botproof · cited by 52
Cited by5
Results whose statement or proof uses this declaration.
- exists_continuous_zero_one_of_isClosedproof · cited by 10
- ShrinkingLemma.PartialRefinement.exists_gtproof · cited by 1
- exists_mem_nhdsSet_isClosed_subsetproof · cited by 1
- exists_contMDiffMap_zero_one_nhds_of_isClosedproof · cited by 1
- Disjoint.hasSeparatingCover_closed_gdelta_rightproof · cited by 0