Theorems · Theorem · general topology
lim_eq_iff
∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] {f : Filter X} [f.NeBot],
(∃ x, f ≤ nhds x) → ∀ {x : X}, f.lim = x ↔ f ≤ nhds x- Defined in
- Mathlib.Topology.Separation.Hausdorff
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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
- nhdsstatement and proof · cited by 5,554
- T2Spacestatement and proof · cited by 1,351
- Filter.NeBotstatement and proof · cited by 853
- Filter.limstatement and proof · cited by 10
- lim_eqproof · cited by 6
- le_nhds_limproof · cited by 5
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