Theorems · Definition · general topology

PartialHomeomorph.toHomeomorphOfSourceEqUnivTargetEqUniv

{X : Type u_1} →
  {Y : Type u_3} →
    [inst : TopologicalSpace X] →
      [inst_1 : TopologicalSpace Y] → (e : PartialHomeomorph X Y) → e.source = Set.univ → e.target = Set.univ → X ≃ₜ Y

If a partial homeomorphism has source and target equal to univ, then it induces a homeomorphism between the whole spaces, expressed in this definition.

Defined in

Mathlib.Topology.PartialHomeomorph.Basic

Cited by

2 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace