Theorems · Theorem · general topology
tendsto_nhdsWithin_mono_left
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] {f : α → β} {a : α} {s t : Set α} {l : Filter β},
s ⊆ t → Filter.Tendsto f (nhdsWithin a t) l → Filter.Tendsto f (nhdsWithin a s) l- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 64 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.
Cites7
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
- Filter.Tendstostatement and proof · cited by 3,814
- nhdsWithinstatement and proof · cited by 1,912
- Filter.Tendsto.mono_leftproof · cited by 125
- nhdsWithin_monoproof · cited by 82
Cited by5
Results whose statement or proof uses this declaration.
- ContinuousOn.ifproof · cited by 4
- hasDerivWithinAt_Iic_of_tendsto_derivproof · cited by 1
- tendsto_sub_mul_tsum_nat_cpowproof · cited by 1
- Real.not_differentiableAt_inv_log_zeroproof · cited by 1
- hasDerivWithinAt_Ici_of_tendsto_derivproof · cited by 1