Theorems · Theorem · general topology

Homeomorph.comp_continuousOn_iff

∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_4} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] (h : X ≃ₜ Y) (f : Z → X) (s : Set Z), ContinuousOn (⇑h ∘ f) s ↔ ContinuousOn f s

Defined in

Mathlib.Topology.Homeomorph.Lemmas

Cited by

4 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace