Theorems · Theorem · general topology

Topology.IsEmbedding.discreteTopology

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

The topology induced under an inclusion f : X → Y from a discrete topological space Y is the discrete topology on X. See also DiscreteTopology.of_continuous_injective.

Defined in

Mathlib.Topology.Maps.Basic

Cited by

6 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceDiscreteTopology