Browse Hierarchy MTH723P: Metric Spaces and Topology

We have learnt how to measure distance on the real line (using the absolute value) and between two points on the plane (applying the Pythagorean Theorem). But can we measure distance between two vectors in a multidimensional Euclidean space, or between two square matrices, or perhaps two functions? The answer is, yes, we can. In this module we study metric spaces which are sets of mathematical objects, such as numbers, vectors, matrices, and functions, equipped with the geometric concept of distance (metric). Inside the universe of a Metric Space, we shall generalize the concepts of convergence and continuity, ideas studied in real analysis and explore the foundations of continuous mathematics. We shall discuss Fixed Point Theorems which play an important role for proving the existence of solutions of differential equations and equilibrium points in economic markets.