Theorems · Theorem · general topology

Set.UniformEquicontinuous.closure

∀ {α : Type u_6} {β : Type u_8} [uα : UniformSpace α] [uβ : UniformSpace β] {A : Set (β → α)},
  A.UniformEquicontinuous → (closure A).UniformEquicontinuous

If a set of functions is uniformly equicontinuous, its closure for the product topology is also uniformly equicontinuous.

Defined in: Mathlib.Topology.UniformSpace.Equicontinuity
Cited by: 0 results in Mathlib
Foundations: Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: UniformSpace UniformSpace

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Setstatement and proof · cited by 53,352
UniformSpacestatement and proof · cited by 2,040
closurestatement · cited by 1,254
continuous_idproof · cited by 192
Set.UniformEquicontinuousstatement and proof · cited by 3
UniformEquicontinuous.closure'proof · cited by 1

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