Suppose that F: U subset of R^n into R^m, with U open. If F is Lipshitz continuous at x in the set of U show that F is continuous at x. Our teacher said this was trivial, but I of course cannot figure it out.
Follow Math Help Forum on Facebook and Google+
Originally Posted by jburks100 Suppose that F: U subset of R^n into R^m, with U open. If F is Lipshitz continuous at x in the set of U show that F is continuous at x. Our teacher said this was trivial, but I of course cannot figure it out. For to be Lipschitz continuous, then such that . Therefore, let and thus So is continuous at .
View Tag Cloud