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Theorems · Theorem · general topology

CauchySeq.prodMk

∀ {α : Type u} {β : Type v} [uniformSpace : UniformSpace α] {γ : Type u_1} [inst : UniformSpace β] [inst_1 : Preorder γ]
  {u : γ → α} {v : γ → β}, CauchySeq u → CauchySeq v → CauchySeq fun x => (u x, v x)
Defined in
Mathlib.Topology.UniformSpace.Cauchy
Cited by
2 results in Mathlib
Foundations
Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpaceUniformSpacePreorder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CauchySeq.add · cited by 2CauchySeq.addCauchySeq.mul · cited by 1CauchySeq.mulPreorder · cited by 7952PreorderUniformSpace · cited by 2040UniformSpaceCauchySeq · cited by 131CauchySeqFilter.Tendsto.prodMk · cited by 35Tendsto.prodMkFilter.tendsto_map · cited by 26Filter.tendsto_mapCauchy.mono · cited by 6Cauchy.monoCauchy.prod · cited by 4Cauchy.prodCauchySeq.prodMkCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.