Theorems · Theorem · general topology
OrderIso.map_atTop
∀ {α : Type u_3} {β : Type u_4} [inst : Preorder α] [inst_1 : Preorder β] (e : α ≃o β),
Filter.map (⇑e) Filter.atTop = Filter.atTop- Defined in
- Mathlib.Order.Filter.AtTopBot.Map
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Filterstatement and proof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Filter.atTopstatement and proof · cited by 2,405
- OrderIsostatement and proof · cited by 874
- Filter.mapstatement and proof · cited by 819
- OrderIso.surjectiveproof · cited by 28
- Filter.map_comap_of_surjectiveproof · cited by 11
- OrderIso.comap_atTopproof · cited by 6
Cited by11
Results whose statement or proof uses this declaration.
- OrderIso.map_atBotproof · cited by 4
- OrderIso.tendsto_atTopproof · cited by 3
- AffineSpace.asymptoticNhds_smulproof · cited by 2
- HasSum.sumproof · cited by 2
- HasProd.sumproof · cited by 2
- Real.map_exp_atTopproof · cited by 2
- Real.map_sqrt_atTopproof · cited by 1
- Filter.map_inv_atTopproof · cited by 1
- Filter.map_neg_atTopproof · cited by 1
- Filter.neg_atTopproof · cited by 0
- Filter.inv_atTopproof · cited by 0