Theorems · Theorem · general topology
Filter.tendsto_inf
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {x : Filter α} {y₁ y₂ : Filter β},
Filter.Tendsto f x (y₁ ⊓ y₂) ↔ Filter.Tendsto f x y₁ ∧ Filter.Tendsto f x y₂- Defined in
- Mathlib.Order.Filter.Tendsto
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Filter.Tendstostatement · cited by 3,814
- Filter.mapproof · cited by 819
Cited by23
Results whose statement or proof uses this declaration.
- Filter.Tendsto.prodMkproof · cited by 35
- Filter.Tendsto.infproof · cited by 32
- tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_withinproof · cited by 28
- UniformContinuous.prodMkproof · cited by 18
- ContinuousWithinAt.tendsto_nhdsWithinproof · cited by 16
- Filter.Tendsto.not_tendstoproof · cited by 14
- Filter.tendsto_iff_seq_tendstoproof · cited by 5
- TendstoLocallyUniformlyOn.smul₀_of_isBoundedUnderproof · cited by 4
- Bundle.Trivialization.tendsto_nhds_iffproof · cited by 3
- TendstoLocallyUniformlyOn.inv₀_of_disjointproof · cited by 3
- ClusterPt.exists_seq_tendstoproof · cited by 2
- UniformContinuousOn.compproof · cited by 2