Theorems · Theorem · general topology
CauchySeq.comp_tendsto
∀ {α : Type u} {β : Type v} [uniformSpace : UniformSpace α] {γ : Type u_1} [inst : Preorder β]
[inst_1 : SemilatticeSup γ] [Nonempty γ] {f : β → α},
CauchySeq f → ∀ {g : γ → β}, Filter.Tendsto g Filter.atTop Filter.atTop → CauchySeq (f ∘ g)- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- UniformSpacestatement and proof · cited by 2,040
- le_rflproof · cited by 1,558
- le_transproof · cited by 985
- SemilatticeSupstatement and proof · cited by 785
- Filter.Tendsto.compproof · cited by 560
- CauchySeqstatement and proof · cited by 131
- Filter.prod_le_prodproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- CauchySeq.comp_injectiveproof · cited by 1
- cauchySeq_shiftproof · cited by 1
- NormedAddCommGroup.cauchy_series_of_le_geometric'proof · cited by 1