Theorems · Theorem · general topology

continuousWithinAt_iff_continuousAt_domRestrict

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] (f : α → β) {x : α}
  {s : Set α} (h : x ∈ s), ContinuousWithinAt f s x ↔ ContinuousAt (s.domRestrict f) ⟨x, h⟩

Defined in

Mathlib.Topology.ContinuousOn

Cited by

4 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace