Theorems · Theorem · general topology
Filter.tendsto_Ioi_atTop
∀ {α : Type u_3} {β : Type u_4} [inst : Preorder α] [IsDirectedOrder α] {a : α} {f : β → ↑(Set.Ioi a)} {l : Filter β},
Filter.Tendsto f l Filter.atTop ↔ Filter.Tendsto (fun x => ↑(f x)) l Filter.atTop- Defined in
- Mathlib.Order.Filter.AtTopBot.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderIsDirectedOrder
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Set.Elemstatement and proof · cited by 7,166
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Set.Ioistatement and proof · cited by 1,463
- IsDirectedOrderstatement and proof · cited by 316
- Filter.tendsto_comap_iffproof · cited by 55
- Filter.atTop_Ioi_eqproof · cited by 1
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