Theorems · Theorem · general topology
ContinuousAt.tendsto
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {x : X},
ContinuousAt f x → Filter.Tendsto f (nhds x) (nhds (f x))- Defined in
- Mathlib.Topology.Continuous
- Cited by
- 103 results in Mathlib
- Foundations
- Depth 20 from the axioms, rests on 95 definitions · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- ContinuousAtstatement and proof · cited by 697
Cited by103
Results whose statement or proof uses this declaration.
- HasFDerivAt.compproof · cited by 50
- HasDerivAt.compproof · cited by 43
- HasStrictFDerivAt.compproof · cited by 37
- HasDerivAt.comp_hasFDerivAtproof · cited by 20
- Filter.Tendsto.powproof · cited by 16
- HasDerivAt.scompproof · cited by 11
- Filter.Tendsto.apply_nhdsproof · cited by 11
- uniformContinuous_of_continuousAt_zeroproof · cited by 11
- Antitone.map_limsSup_of_continuousAtproof · cited by 6
- StieltjesFunction.measure_singletonproof · cited by 6
- ContinuousAt.eventually_neproof · cited by 6
- HasDerivAt.lhopital_zero_right_on_Iooproof · cited by 5