Theorems · Theorem · general topology

Set.MapsTo.closure_of_continuousOn

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {s : Set α}
  {t : Set β}, Set.MapsTo f s t → ContinuousOn f (closure s) → Set.MapsTo f (closure s) (closure t)

Defined in

Mathlib.Topology.ContinuousOn

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace