Theorems · Theorem · general topology

Set.EquicontinuousOn.continuousOn_of_mem

∀ {X : Type u_3} {α : Type u_6} [tX : TopologicalSpace X] [uα : UniformSpace α] {H : Set (X → α)} {S : Set X},
  H.EquicontinuousOn S → ∀ {f : X → α}, f ∈ H → ContinuousOn f S

Defined in: Mathlib.Topology.UniformSpace.Equicontinuity
Cited by: 0 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace UniformSpace

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Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
UniformSpacestatement and proof · cited by 2,040
ContinuousOnstatement · cited by 1,411
Set.EquicontinuousOnstatement and proof · cited by 3
EquicontinuousOn.continuousOnproof · cited by 1

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