Theorems · Theorem · general topology
Filter.atTop_Ioi_eq
∀ {α : Type u_3} [inst : Preorder α] [IsDirectedOrder α] (a : α), Filter.atTop = Filter.comap Subtype.val Filter.atTopThe atTop filter for ↑(Ioi a) comes from the atTop filter in the ambient order.
- Defined in
- Mathlib.Order.Filter.AtTopBot.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderIsDirectedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.Elemproof · cited by 7,166
- Filter.atTopstatement and proof · cited by 2,405
- Set.Ioistatement and proof · cited by 1,463
- IsEmptyproof · cited by 759
- Filter.comapstatement and proof · cited by 546
- IsDirectedOrderstatement and proof · cited by 316
- isEmpty_or_nonemptyproof · cited by 269
- Subtype.coe_injectiveproof · cited by 205
- Set.Ici_subset_Ioiproof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- Filter.tendsto_Ioi_atTopproof · cited by 0