Theorems · Definition · general topology

OpenPartialHomeomorph.homeomorphOfImageSubsetSource

{X : Type u_1} →
  {Y : Type u_3} →
    [inst : TopologicalSpace X] →
      [inst_1 : TopologicalSpace Y] →
        (e : OpenPartialHomeomorph X Y) → {s : Set X} → {t : Set Y} → s ⊆ e.source → ↑e '' s = t → ↑s ≃ₜ ↑t

The homeomorphism obtained by restricting an OpenPartialHomeomorph to a subset of the source.

Defined in

Mathlib.Topology.OpenPartialHomeomorph.Basic

Cited by

2 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace