Theorems · Theorem · general topology

Continuous.tendsto_nhdsSet_nhds

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {s : Set α} {b : β}
  {f : α → β}, Continuous f → Set.EqOn f (fun x => b) s → Filter.Tendsto f (nhdsSet s) (nhds b)

Defined in

Mathlib.Topology.ContinuousOn

Cited by

2 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace