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Theorems · Theorem · general topology

tendsto_prod_uniformity_fst

∀ {α : Type ua} {β : Type ub} [inst : UniformSpace α] [inst_1 : UniformSpace β],
  Filter.Tendsto (fun p => (p.1.1, p.2.1)) (uniformity (α × β)) (uniformity α)
Defined in
Mathlib.Topology.UniformSpace.Basic
Cited by
1 results in Mathlib
Foundations
Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpaceUniformSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

uniformContinuous_fst · cited by 8uniformContinuous_fstFilter.Tendsto · cited by 3814Filter.TendstoUniformSpace · cited by 2040UniformSpacele_trans · cited by 985le_transuniformity · cited by 765uniformityinf_le_left · cited by 286inf_le_leftFilter.map_mono · cited by 63Filter.map_monoFilter.map_comap_le · cited by 10Filter.map_comap_letendsto_prod_uniformity_fstCITED BYCITES

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Cited by1

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