Theorems · Theorem · general topology
Filter.Tendsto.limUnder_eq
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [T2Space X] {x : X} {f : Filter Y} [f.NeBot] {g : Y → X},
Filter.Tendsto g f (nhds x) → f.limUnder g = x- Defined in
- Mathlib.Topology.Separation.Hausdorff
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 92 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
- Filter.Tendstostatement and proof · cited by 3,814
- T2Spacestatement and proof · cited by 1,351
- Filter.NeBotstatement and proof · cited by 853
- Filter.limUnderstatement · cited by 47
- lim_eqproof · cited by 6
Cited by19
Results whose statement or proof uses this declaration.
- IsDenseInducing.extend_eq_of_tendstoproof · cited by 6
- UpperHalfPlane.IsZeroAtImInfty.valueAtInfty_eq_zeroproof · cited by 5
- Complex.differentiableOn_update_limUnder_of_isLittleOproof · cited by 4
- Real.tendsto_eulerMascheroniSeqproof · cited by 3
- Function.Periodic.cuspFunction_zero_of_zero_at_infproof · cited by 3
- UpperHalfPlane.cuspFunction_apply_zeroproof · cited by 3
- CircleDeg1Lift.translationNumber_eq_of_tendsto_auxproof · cited by 2
- Function.Periodic.cuspFunction_addproof · cited by 2
- Function.Periodic.cuspFunction_smulproof · cited by 2
- UpperHalfPlane.qExpansion_oneproof · cited by 2
- UpperHalfPlane.qExpansion_zeroproof · cited by 2
- SimpleGraph.isGLB_turanDensityproof · cited by 2