Theorems · Theorem · general topology

extendFrom_extends

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [T2Space Y] {f : X → Y}
  {A : Set X}, ContinuousOn f A → ∀ x ∈ A, extendFrom A f x = f x

Defined in

Mathlib.Topology.ExtendFrom

Cited by

2 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceT2Space