Theorems · Inductive type · general topology

Topology.IsEmbedding

{X : Type u_1} → {Y : Type u_2} → [tX : TopologicalSpace X] → [tY : TopologicalSpace Y] → (X → Y) → Prop

A function between topological spaces is an embedding if it is injective, and for all s : Set X, s is open iff it is the preimage of an open set.

Defined in

Mathlib.Topology.Defs.Induced

Cited by

294 results in Mathlib

Foundations

Depth 1 from the axioms, rests on 2 definitions · uses no axioms

Assumes

TopologicalSpaceTopologicalSpace