Theorems · Definition · general topology

Topology.IsOpenEmbedding.toOpenPartialHomeomorph

{X : Type u_1} →
  {Y : Type u_3} →
    [inst : TopologicalSpace X] →
      [inst_1 : TopologicalSpace Y] →
        (f : X → Y) → Topology.IsOpenEmbedding f → [Nonempty X] → OpenPartialHomeomorph X Y

An open embedding of X into Y, with X nonempty, defines an open partial homeomorphism whose source is all of X. The converse is also true; see OpenPartialHomeomorph.isOpenEmbedding.

Defined in

Mathlib.Topology.OpenPartialHomeomorph.Basic

Cited by

14 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceNonempty