Theorems · Theorem · general topology
Filter.tendsto_iInf
∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_4} {f : α → β} {x : Filter α} {y : ι → Filter β},
Filter.Tendsto f x (⨅ i, y i) ↔ ∀ (i : ι), Filter.Tendsto f x (y i)- Defined in
- Mathlib.Order.Filter.Tendsto
- Cited by
- 13 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.
Cites4
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
- iInfstatement · cited by 1,690
- Filter.mapproof · cited by 819
Cited by13
Results whose statement or proof uses this declaration.
- Filter.tendsto_atTop_atTopproof · cited by 11
- Filter.tendsto_atTop_atTop_of_monotoneproof · cited by 8
- Filter.tendsto_atBotproof · cited by 7
- Filter.tendsto_atBot_atBotproof · cited by 3
- Filter.tendsto_atBot_atBot_of_monotoneproof · cited by 3
- uniformContinuous_sInf_rngproof · cited by 2
- isAddFoelner_iff_tendstoproof · cited by 1
- Filter.tendsto_iInf_iInfproof · cited by 1
- tendsto_nhds_bot_monoproof · cited by 1
- uniformContinuous_iInf_rngproof · cited by 1
- equicontinuousWithinAt_iInf_rngproof · cited by 0
- uniformEquicontinuousOn_iInf_rngproof · cited by 0