Theorems · Theorem · general topology

ContinuousOn.continuousAt_indicator

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {s : Set α}
  [inst_2 : Zero β], ContinuousOn f (interior s) → ∀ {x : α}, x ∉ frontier s → ContinuousAt (s.indicator f) x

Defined in

Mathlib.Topology.Algebra.Indicator

Cited by

1 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceZero