If f A B and g: C B such that A C C and for each a A we have f(a) = g(a) then g extends f. We also say that f extends to g. Assume that f: S R is a uniformly continuous function defined on a subset S of a metric space M. (a) Prove that f extends to a uniformly continuous function 7:5 R. (b) Prove that is the unique continuous extension of f to a function defined on 5. (c) Prove the same things when R is replaced with a complete metric space N.