Theorems · Theorem · general topology

ContinuousWithinAt.mem_closure

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {s : Set α}
  {x : α} {t : Set β}, ContinuousWithinAt f s x → x ∈ closure s → Set.MapsTo f s t → f x ∈ closure t

Defined in

Mathlib.Topology.ContinuousOn

Cited by

4 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace