Theorems · Theorem · general topology

SeparationQuotient.map_unique

∀ {α : Type u} {β : Type v} [inst : UniformSpace α] [inst_1 : UniformSpace β] {f : α → β},
  UniformContinuous f →
    ∀ {g : SeparationQuotient α → SeparationQuotient β},
      SeparationQuotient.mk ∘ f = g ∘ SeparationQuotient.mk → SeparationQuotient.map f = g

Defined in

Mathlib.Topology.UniformSpace.Separation

Cited by

2 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceUniformSpace