Theorems · Theorem · general topology
eventually_mem_of_tendsto_nhdsWithin
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] {f : β → α} {a : α} {s : Set α} {l : Filter β},
Filter.Tendsto f l (nhdsWithin a s) → ∀ᶠ (i : β) in l, f i ∈ s- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 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.
Cites11
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 and proof · cited by 8,121
- Set.univproof · cited by 3,945
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.Eventuallystatement and proof · cited by 3,134
- IsOpenproof · cited by 2,400
- nhdsWithinstatement and proof · cited by 1,912
- Set.mem_univproof · cited by 416
- isOpen_univproof · cited by 112
- nhdsWithin_eqproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- tendsto_nhdsWithin_iffproof · cited by 37
- IsUnifLocDoublingMeasure.tendsto_closedBall_filterAtproof · cited by 3
- exists_dist_slope_lt_pairwiseDisjoint_hasSumproof · cited by 1