Theorems · Theorem · general topology

Continuous.measurableEmbedding

∀ {γ : Type u_3} {β : Type u_5} [inst : MeasurableSpace β] [tβ : TopologicalSpace β] [T2Space β] {f : γ → β}
  [BorelSpace β] [inst_3 : TopologicalSpace γ] [PolishSpace γ] [inst_5 : MeasurableSpace γ] [BorelSpace γ],
  Continuous f → Function.Injective f → MeasurableEmbedding f

An injective continuous function on a Polish space is a measurable embedding.

Defined in

Mathlib.MeasureTheory.Constructions.Polish.Basic

Cited by

1 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceT2SpaceBorelSpaceTopologicalSpacePolishSpaceMeasurableSpaceBorelSpace