Recent content by h-simplex

So I was flipping through Lang's Undergraduate Analysis and noticed the absence of the important concept of metric spaces. I checked the index and was referred to problem 2, Chapter 6 Section 2. There he defines a metric space, what a bounded metric is, and gives a few straightforward problems...

Homework Statement I want to prove this proposition: Let f: M \rightarrow N be a uniformly continuous bijection between metric spaces. If M is complete, then N is complete.The Attempt at a Solution I have a 'partial' solution, whose legitimacy hinges upon a claim that I am unable to prove...