Theorems · Theorem · general topology
exists_mem_nhds_isClosed_subset
∀ {X : Type u_1} [inst : TopologicalSpace X] [RegularSpace X] {x : X} {s : Set X},
s ∈ nhds x → ∃ t ∈ nhds x, IsClosed t ∧ t ⊆ s- Defined in
- Mathlib.Topology.Separation.Regular
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceRegularSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- nhdsstatement and proof · cited by 5,554
- Disjointproof · cited by 2,201
- IsClosedstatement and proof · cited by 1,639
- closureproof · cited by 1,254
- nhdsSetproof · cited by 267
- List.TFAE.outproof · cited by 177
- Filter.lift'proof · cited by 99
- RegularSpacestatement and proof · cited by 63
- regularSpace_TFAEproof · cited by 6
Cited by9
Results whose statement or proof uses this declaration.
- closed_nhds_basisproof · cited by 12
- cauchySeq_finset_iff_tprod_vanishingproof · cited by 3
- cauchySeq_finset_iff_tsum_vanishingproof · cited by 3
- exists_closed_nhds_one_inv_eq_mul_subsetproof · cited by 3
- exists_closed_nhds_zero_neg_eq_add_subsetproof · cited by 3
- setOfPred_riemannianEDist_lt_subset_nhdsproof · cited by 2
- disjoint_nested_nhds_of_not_inseparableproof · cited by 1
- Filter.HasBasis.hasBasis_of_isDenseInducingproof · cited by 0
- Bornology.IsVonNBounded.closureproof · cited by 0