Theorems · Theorem · general topology

ContinuousWithinAt.tendsto_nhdsWithin_image

∀ {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 → Filter.Tendsto f (nhdsWithin x s) (nhdsWithin (f x) (f '' s))

Defined in

Mathlib.Topology.ContinuousOn

Cited by

3 results in Mathlib

Foundations

Depth 53 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace