Mappings of Metric Spaces

In the last chapter you learned about some of the “geometry” of metric spaces. These geometrical ideas are more general than those you studied in high school, such as the congruence or similarity of triangles. They underlie all of geometry and are fundamental for the study of analysis, the branch of mathematics that develops and extends the ideas of calculus. In calculus you studied derivatives and integrals, which in turn were based on the idea of limits. It is possible to define limits in a metric space, but I will examine a more basic concept, that of continuous mappings of metric spaces.