Theorems · Definition · general topology

Equiv.toHomeomorphOfIsInducing

{X : Type u_1} →
  {Y : Type u_2} →
    [inst : TopologicalSpace X] → [inst_1 : TopologicalSpace Y] → (f : X ≃ Y) → Topology.IsInducing ⇑f → X ≃ₜ Y

An inducing equiv between topological spaces is a homeomorphism.

Defined in

Mathlib.Topology.Homeomorph.Defs

Cited by

8 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace