Theorems · Definition · general topology

Equiv.toHomeomorph

{X : Type u_1} →
  {Y : Type u_2} →
    [inst : TopologicalSpace X] →
      [inst_1 : TopologicalSpace Y] → (e : X ≃ Y) → (∀ (s : Set Y), IsOpen (⇑e ⁻¹' s) ↔ IsOpen s) → X ≃ₜ Y

An equivalence between topological spaces respecting openness is a homeomorphism.

Defined in

Mathlib.Topology.Homeomorph.Defs

Cited by

8 results in Mathlib

Foundations

Depth 18 from the axioms · uses Quot.sound

Assumes

TopologicalSpaceTopologicalSpace