Let (X,p) be a metric space and let S Í X be totally bounded. Argue that the closure of S is totally bounded.
Follow Math Help Forum on Facebook and Google+
Originally Posted by jburks100 Let (X,p) be a metric space and let S IÍ X be totally bounded. Argue that the closure of S is totally bounded. Suppose that is not totally bounded. There is such that there is no for . But there must a for . So some such that is not in the for . Let . You need to argue that . But must contain a point in . Now prove that is a contradiction.
View Tag Cloud