Theorems · Theorem · general topology

ContinuousOn.continuousAt

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

Defined in

Mathlib.Topology.ContinuousOn

Cited by

33 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace