1. The problem statement, all variables and given/known data Let f : A --> Y be a continuous function, where A is a subset of X and Y is Haussdorf. Show that, if f can be extended to a continuous function g : Cl(A) --> Y, then g is uniquely determined by f. 3. The attempt at a solution I think I can solve this on my own, but I got a bit stuck, perhaps I didn't understand the problem right, so let me check. I assume an extension of a function in this case means that for any x in A, f(x) = g(x), and further on, I assume that g is uniquely determined by f if, for any x in Cl(A) , f(x) = g(x), too. Am I right on this one?