Theorems · Theorem · general topology
Filter.tendsto_map
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {x : Filter α}, Filter.Tendsto f x (Filter.map f x)- Defined in
- Mathlib.Order.Filter.Tendsto
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 14 from the axioms · 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.
- Filterstatement and proof · cited by 8,121
- Filter.Tendstostatement · cited by 3,814
- le_reflproof · cited by 2,061
- Filter.mapstatement and proof · cited by 819
Cited by26
Results whose statement or proof uses this declaration.
- Filter.prod_map_map_eqproof · cited by 17
- HasFDerivAtFilter.negproof · cited by 7
- HasFDerivAtFilter.const_smulproof · cited by 5
- HasFDerivAtFilter.starproof · cited by 4
- HasFDerivAtFilter.sndproof · cited by 3
- mem_tangentConeAt_of_frequentlyproof · cited by 3
- Filter.EventuallyConst.comp₂proof · cited by 3
- isProperMap_of_comp_of_surjproof · cited by 2
- HasFDerivAtFilter.fstproof · cited by 2
- IsUnit.smul_tendsto_smul_iffproof · cited by 2
- Filter.map_piMap_piproof · cited by 2
- CauchySeq.prodMkproof · cited by 2