Theorems · Theorem · general topology

continuousWithinAt_sdiff_self

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

See also continuousWithinAt_sdiff_singleton for the case of s \ {y}, but requiring T1Space α.

Defined in

Mathlib.Topology.ContinuousOn

Cited by

6 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace