Theorems · Theorem · general topology

ContinuousAt.codRestrict

∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {t : Set Y}
  (h1 : ∀ (x : X), f x ∈ t) {x : X}, ContinuousAt f x → ContinuousAt (Set.codRestrict f t h1) x

Alias of the reverse direction of continuousAt_codRestrict_iff.

Defined in

Mathlib.Topology.Constructions

Cited by

3 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace