Theorems · Theorem · general topology
UniformEquicontinuous.uniformContinuous
∀ {ι : Type u_1} {α : Type u_6} {β : Type u_8} [uα : UniformSpace α] [uβ : UniformSpace β] {F : ι → β → α},
UniformEquicontinuous F → ∀ (i : ι), UniformContinuous (F i)Each function of a uniformly equicontinuous family is uniformly continuous.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- UniformSpaceUniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.ofPredproof · cited by 6,101
- UniformSpacestatement and proof · cited by 2,040
- uniformityproof · cited by 765
- UniformContinuousstatement · cited by 410
- Filter.mem_of_supersetproof · cited by 308
- Filter.mem_mapproof · cited by 63
- UniformEquicontinuousstatement and proof · cited by 35
Cited by1
Results whose statement or proof uses this declaration.
- Set.UniformEquicontinuous.uniformContinuous_of_memproof · cited by 0