Theorems · Theorem · general topology
tendsto_const_nhds
∀ {X : Type u} [inst : TopologicalSpace X] {α : Type u_1} {x : X} {f : Filter α},
Filter.Tendsto (fun x_1 => x) f (nhds x)- Defined in
- Mathlib.Topology.Neighborhoods
- Cited by
- 330 results in Mathlib
- Foundations
- Depth 61 from the axioms, rests on 637 definitions · uses propext, Quot.sound
- Assumes
- TopologicalSpace
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.
- Setproof · 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
- IsOpenproof · cited by 2,400
- Filter.univ_mem'proof · cited by 1,672
- tendsto_nhdsproof · cited by 3
Cited by330
Results whose statement or proof uses this declaration.
- continuousAt_constproof · cited by 59
- MeasureTheory.stronglyMeasurable_constproof · cited by 47
- HasStrictFDerivAt.hasFDerivAtproof · cited by 43
- tendsto_nhds_of_eventually_eqproof · cited by 21
- Filter.Tendsto.const_subproof · cited by 16
- Filter.Tendsto.sub_constproof · cited by 16
- tendsto_atTop_of_eventually_constproof · cited by 14
- hasSum_geometric_of_lt_oneproof · cited by 14
- hasSum_zeroproof · cited by 13
- MeasureTheory.SimpleFunc.stronglyMeasurableproof · cited by 13
- ENNReal.Tendsto.const_mulproof · cited by 13
- tendsto_sub_nhds_zero_iffproof · cited by 12
Showing the 200 most cited of 330.