Theorems · Theorem · general topology
lim_eq
∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] {f : Filter X} {x : X} [f.NeBot], f ≤ nhds x → f.lim = x- Defined in
- Mathlib.Topology.Separation.Hausdorff
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- tendsto_nhds_uniqueproof · cited by 118
- Filter.limstatement · cited by 10
- le_nhds_limproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Filter.Tendsto.limUnder_eqproof · cited by 19
- leftLim_eq_of_tendstoproof · cited by 5
- Ultrafilter.lim_eq_iff_le_nhdsproof · cited by 2
- lim_nhdsproof · cited by 1
- lim_nhdsWithinproof · cited by 1
- lim_eq_iffproof · cited by 0