Theorems · Theorem · general topology

continuousAt_iff_punctured_nhds

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {a : α},
  ContinuousAt f a ↔ Filter.Tendsto f (nhdsWithin a {a}ᶜ) (nhds (f a))

Defined in

Mathlib.Topology.NhdsWithin

Cited by

4 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace