Theorems · Theorem · general topology

ContinuousAt.continuousWithinAt

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {s : Set α}
  {x : α}, ContinuousAt f x → ContinuousWithinAt f s x

Defined in

Mathlib.Topology.ContinuousOn

Cited by

102 results in Mathlib

Foundations

Depth 65 from the axioms, rests on 766 definitions · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace