Theorems · Theorem · general topology
eventually_eventually_nhdsWithin
∀ {α : Type u_1} [inst : TopologicalSpace α] {a : α} {s : Set α} {p : α → Prop},
(∀ᶠ (y : α) in nhdsWithin a s, ∀ᶠ (x : α) in nhdsWithin y s, p x) ↔ ∀ᶠ (x : α) in nhdsWithin a s, p x- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 70 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.
Cites10
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
- nhdsproof · cited by 5,554
- Filter.Eventuallystatement and proof · cited by 3,134
- nhdsWithinstatement and proof · cited by 1,912
- Filter.Eventually.monoproof · cited by 646
- inf_le_leftproof · cited by 286
- Filter.Eventually.filter_monoproof · cited by 84
- Filter.Eventually.self_of_nhdsproof · cited by 38
- eventually_nhds_nhdsWithinproof · cited by 7
Cited by12
Results whose statement or proof uses this declaration.
- ContDiffWithinAt.eventuallyproof · cited by 9
- Filter.EventuallyEq.fderivWithin'proof · cited by 5
- ContMDiffWithinAt.mlieBracketWithin_vectorFieldproof · cited by 3
- Filter.EventuallyEq.mlieBracketWithin_vectorField'proof · cited by 2
- MeromorphicOn.codiscrete_setOfPred_meromorphicOrderAt_eq_zero_or_topproof · cited by 2
- VectorField.leibniz_identity_mlieBracketWithin_applyproof · cited by 1
- fderivWithin_fderivWithin_eq_of_mem_nhdsWithinproof · cited by 1
- eventually_mem_nhdsWithin_iffproof · cited by 1
- ContDiffWithinAt.restrictScalars_iteratedFDerivWithin_eventuallyEqproof · cited by 1
- eventually_nhdsWithin_eventually_nhds_iff_of_isOpenproof · cited by 1
- Filter.EventuallyEq.extDerivWithin'proof · cited by 1
- Filter.EventuallyEq.ftaylorSeriesWithinproof · cited by 0