Learning Outcomes:
The student should learn how to recognize, manipulate and apply the foundational concepts of metric analysis: metric spaces and metrics; isometries; the distance between points and sets; the boundary, closure and interior of sets; open and closed sets and balls; the topology of a metric space, convergence of sequences and continuity of functions; Cauchy sequences; compactness, completeness, fixed point theorems and a selection of additional topics as covered in the course (for example, normed vector spaces, isolated points and accumulation points, the diameter of a set, connectedness).