Theorems · Theorem · general topology
tendsto_const_nhds_iff
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [T1Space X] {l : Filter Y} [l.NeBot] {c d : X},
Filter.Tendsto (fun x => c) l (nhds d) ↔ c = d- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 3,814
- Filter.NeBotstatement and proof · cited by 853
- T1Spacestatement and proof · cited by 275
- Filter.map_constproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AddCircle.ae_empty_or_univ_of_forall_vadd_ae_eq_selfproof · cited by 2