DiscreteUniformity.uniformContinuous

∀ (X : Type u_1) [u : UniformSpace X] [DiscreteUniformity X] {Y : Type u_2} [inst : UniformSpace Y] (f : X → Y),
  UniformContinuous f

On a space with a discrete uniformity, any function is uniformly continuous.

Defined in: Mathlib.Topology.UniformSpace.DiscreteUniformity
Cited by: 0 results in Mathlib
Foundations: Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: UniformSpace DiscreteUniformity UniformSpace

Around this declaration

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

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.

Nothing cites this yet.