Theorems · Theorem · general topology
OnePoint.tendsto_nhds_infty
∀ {X : Type u_1} [inst : TopologicalSpace X] {α : Type u_3} {f : OnePoint X → α} {l : Filter α},
Filter.Tendsto f (nhds OnePoint.infty) l ↔
∀ s ∈ l, f OnePoint.infty ∈ s ∧ ∃ t, IsClosed t ∧ IsCompact t ∧ Set.MapsTo (f ∘ OnePoint.some) tᶜ s- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Compl.complstatement and proof · cited by 2,925
- IsClosedstatement and proof · cited by 1,639
- IsCompactstatement and proof · cited by 1,282
- Set.MapsTostatement and proof · cited by 732
- OnePointstatement and proof · cited by 126
- OnePoint.inftystatement and proof · cited by 102
- OnePoint.somestatement and proof · cited by 76
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