Metrics

Summary

In this chapter, we have defined the terms metric and metric space and given various examples. We have defined norms on linear spaces and shown that they determine metrics. We have introduced metric subspaces and metric superspaces and metrics on products of metric spaces. We have explained the concept of isometric spaces and have shown that an isometric copy can be made of any given metric space simply be endowing its set of point functions with a suitable metric; we have also shown that this isometric copy of the given space sits inside a naturally defined metric superspace.