f : X → Y is uniformly continuous if ∀ε>0 ∃δ>0 ∀x,y: d(x,y)<δ ⇒ d(f(x),f(y))<ε (same δ works everywhere). Heine: continuous ⇒ uniformly continuous on compact domain.
f : X → Y is uniformly continuous if ∀ε>0 ∃δ>0 ∀x,y: d(x,y)<δ ⇒ d(f(x),f(y))<ε (same δ works everywhere). Heine: continuous ⇒ uniformly continuous on compact domain.