Theorems · Theorem · general topology
Filter.OrderTop.atTop_eq
∀ (α : Type u_6) [inst : PartialOrder α] [inst_1 : OrderTop α], Filter.atTop = pure ⊤
- Defined in
- Mathlib.Order.Filter.AtTopBot.Tendsto
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Quot.sound
- Assumes
- PartialOrderOrderTop
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.
- Setproof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- Filterstatement and proof · cited by 8,121
- PartialOrderstatement and proof · cited by 6,410
- Filter.atTopstatement · cited by 2,405
- Filter.principalproof · cited by 740
- OrderTopstatement and proof · cited by 493
- Filter.principal_singletonproof · cited by 31
- isTop_topproof · cited by 10
- Set.Ici_topproof · cited by 4
- IsTop.atTop_eqproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- tendsto_rightLim_atTop_of_tendstoproof · cited by 2
- Filter.map_card_atTop_of_fintypeproof · cited by 2
- Filter.tendsto_atTop_pureproof · cited by 1
- Filter.atTop_eq_pure_of_isTopproof · cited by 1