Theorems · Theorem · general topology

continuousWithinAt_update_same

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {s : Set α}
  {x : α} [inst_2 : DecidableEq α] {y : β},
  ContinuousWithinAt (Function.update f x y) s x ↔ Filter.Tendsto f (nhdsWithin x (s \ {x})) (nhds y)

Defined in

Mathlib.Topology.Piecewise

Cited by

4 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceDecidableEq