Claremont Center for the Mathematical Sciences

In this expository talk we look at look at two classes of metric spaces lying between the compact metric spaces and the complete metric spaces. The first is the well-known class of UC spaces, best known as the class of spaces on which each continuous function with values in a metric space is uniformly continuous. The second is the class of cofinally complete metric spaces, best known as the class of spaces in which
each “cofinally Cauchy” sequence has a cluster point. We show how these classes are in many ways parallel universes, and explain why.