Theorems · Theorem · general topology
limsup_eq_bot
∀ {α : Type u_2} {β : Type u_3} [inst : CompleteLinearOrder α] [inst_1 : TopologicalSpace α] [FirstCountableTopology α]
[OrderTopology α] {f : Filter β} [CountableInterFilter f] {u : β → α}, Filter.limsup u f = ⊥ ↔ u =ᶠ[f] ⊥- Defined in
- Mathlib.Topology.Order.LiminfLimsup
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- Bot.botstatement and proof · cited by 4,720
- le_antisymmproof · cited by 2,068
- Filter.EventuallyEqstatement and proof · cited by 1,912
- OrderTopologystatement and proof · cited by 1,355
- Filter.Eventually.monoproof · cited by 646
- Eq.leproof · cited by 605
- Filter.Eventually.of_forallproof · cited by 526
- bot_leproof · cited by 306
- Filter.limsupstatement and proof · cited by 226
- CompleteLinearOrderstatement and proof · cited by 126
Cited by3
Results whose statement or proof uses this declaration.
- ENNReal.limsup_const_mulproof · cited by 3
- ENNReal.limsup_eq_zero_iffproof · cited by 1
- liminf_eq_topproof · cited by 0