Assignment:
Q1. If A and U are two subsets of a normed vector space, and U is open, show that A+U is open. Here A+U={a+u | a belongs to A and u belongs to U}.
Q2. Suppose {xn} from n=p to infinity is a non-converging subsequence in a compact set of a metric space. Show that it has two convergent subsequences which converge to distinct limit points.
Provide complete and step by step solution for the question and show calculations and use formulas.