Theorems · Theorem · general topology
exists_mem_nhdsSet_isClosed_subset
∀ {X : Type u_1} [inst : TopologicalSpace X] [NormalSpace X] {u s : Set X},
s ∈ nhdsSet u → IsClosed u → ∃ t ∈ nhdsSet u, IsClosed t ∧ t ⊆ s- Defined in
- Mathlib.Topology.Separation.Regular
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 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
- Filterstatement · cited by 8,121
- LE.le.transproof · cited by 3,151
- IsOpenproof · cited by 2,400
- IsClosedstatement and proof · cited by 1,639
- closureproof · cited by 1,254
- subset_closureproof · cited by 309
- Filter.mem_of_supersetproof · cited by 308
- nhdsSetstatement and proof · cited by 267
- isClosed_closureproof · cited by 195
- NormalSpacestatement and proof · cited by 84
Cited by1
Results whose statement or proof uses this declaration.
- closed_nhdsSet_basisproof · cited by 1