Theorems · Definition · general topology

OpenPartialHomeomorph.ofContinuousOpen

{X : Type u_1} →
  {Y : Type u_3} →
    [inst : TopologicalSpace X] →
      [inst_1 : TopologicalSpace Y] →
        (e : PartialEquiv X Y) → ContinuousOn (↑e) e.source → IsOpenMap ↑e → IsOpen e.source → OpenPartialHomeomorph X Y

A PartialEquiv which is continuous on its source and has open forward map (on its source) and open source is an OpenPartialHomeomorph.

Defined in

Mathlib.Topology.OpenPartialHomeomorph.Basic

Cited by

3 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace