Theorems · Definition · general topology

Homeomorph.toPartialHomeomorphOfImageEq

{X : Type u_1} →
  {Y : Type u_3} →
    [inst : TopologicalSpace X] →
      [inst_1 : TopologicalSpace Y] → (e : X ≃ₜ Y) → (s : Set X) → (t : Set Y) → ⇑e '' s = t → PartialHomeomorph X Y

Interpret a Homeomorph as a PartialHomeomorph by restricting it to a set s in the domain and to t in the codomain.

Defined in

Mathlib.Topology.PartialHomeomorph.Defs

Cited by

7 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace