Theorems · Theorem · general topology

Topology.IsInducing.isEmbedding

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [T0Space X] {f : X → Y},
  Topology.IsInducing f → Topology.IsEmbedding f

A topology inducing map from a T₀ space is a topological embedding.

Defined in

Mathlib.Topology.Separation.Basic

Cited by

5 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceT0Space