Theorems · Theorem · general topology
nhdsWithin_hasBasis
∀ {α : Type u_1} [inst : TopologicalSpace α] {ι : Sort u_5} {p : ι → Prop} {s : ι → Set α} {a : α},
(nhds a).HasBasis p s → ∀ (t : Set α), (nhdsWithin a t).HasBasis p fun i => s i ∩ t- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- nhdsstatement and proof · cited by 5,554
- nhdsWithinstatement · cited by 1,912
- Filter.HasBasisstatement and proof · cited by 604
- Filter.HasBasis.inf_principalproof · cited by 18
Cited by15
Results whose statement or proof uses this declaration.
- mem_nhdsWithin_iff_exists_mem_nhds_interproof · cited by 12
- nhdsWithin_basis_openproof · cited by 6
- Topology.IsInducing.locallyCompactSpaceproof · cited by 4
- balancedCore_mem_nhds_zeroproof · cited by 4
- Filter.HasBasis.exists_inter_eq_singleton_of_mem_discreteproof · cited by 3
- Metric.nhdsWithin_basis_eballproof · cited by 3
- Filter.HasBasis.tangentConeAt_eq_biInter_closureproof · cited by 2
- Metric.nhdsWithin_basis_ballproof · cited by 2
- EReal.nhdsWithin_botproof · cited by 1
- EReal.nhdsWithin_topproof · cited by 1
- SmoothBumpFunction.nhdsWithin_range_basisproof · cited by 1