Theorems · Theorem · general topology

ContinuousWithinAt.image_closure

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {s : Set α},
  (∀ x ∈ closure s, ContinuousWithinAt f s x) → f '' closure s ⊆ closure (f '' s)

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