Question

Suppose −∞ ≤ a < c < b ≤ ∞ and f : (a,b) → R is continuous on (a,b).

(a) If f is uniformly continuous on both (a,c) and (c,b), prove that f is uniformly continuous on (a,b).

Answer 1

i guess you have to show f is uniformly continuous on \( (b-\delta, b + \delta)\)