Theorems · Theorem · general topology
Filter.map_val_Ioi_atTop
∀ {α : Type u_3} [inst : Preorder α] [IsDirectedOrder α] [NoMaxOrder α] (a : α),
Filter.map Subtype.val Filter.atTop = Filter.atTopThe image of the filter atTop on Ioi a under the coercion equals atTop.
- Defined in
- Mathlib.Order.Filter.AtTopBot.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Filterstatement · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Filter.atTopstatement and proof · cited by 2,405
- Set.Ioistatement · cited by 1,463
- Filter.mapstatement and proof · cited by 819
- NoMaxOrderstatement and proof · cited by 340
- IsDirectedOrderstatement and proof · cited by 316
- NoMaxOrder.exists_gtproof · cited by 62
- Set.Ici_subset_Ioiproof · cited by 15
- Filter.map_val_atTop_of_Ici_subsetproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Real.map_exp_atTopproof · cited by 2
- Filter.tendsto_comp_val_Ioi_atTopproof · cited by 1