Theorems · Theorem · general topology
Filter.atBot_Iio_eq
∀ {α : Type u_3} [inst : Preorder α] [IsCodirectedOrder α] (a : α), Filter.atBot = Filter.comap Subtype.val Filter.atBotThe atBot filter for ↑(Iio a) comes from the atBot filter in the ambient order.
- Defined in
- Mathlib.Order.Filter.AtTopBot.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderIsCodirectedOrder
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
- Set.Iiostatement and proof · cited by 1,166
- IsEmptyproof · cited by 759
- Filter.comapstatement and proof · cited by 546
- Filter.atBotstatement and proof · cited by 512
- isEmpty_or_nonemptyproof · cited by 269
- Subtype.coe_injectiveproof · cited by 205
- IsCodirectedOrderstatement and proof · cited by 95
- Filter.comap_mapproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- Filter.tendsto_Iio_atBotproof · cited by 0