Theorems · Theorem · general topology
liminf_eq_top
∀ {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.liminf u f = ⊤ ↔ u =ᶠ[f] ⊤- Defined in
- Mathlib.Topology.Order.LiminfLimsup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- Top.topstatement · cited by 9,680
- Filterstatement and proof · cited by 8,121
- Filter.EventuallyEqstatement · cited by 1,912
- OrderTopologystatement and proof · cited by 1,355
- Filter.liminfstatement · cited by 198
- CompleteLinearOrderstatement and proof · cited by 126
- FirstCountableTopologystatement and proof · cited by 106
- CountableInterFilterstatement and proof · cited by 78
- limsup_eq_botproof · cited by 3
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