There are many ways to measure distance in the spaces in which we live and work. For example, if you want the shortest distance between two geographical places (the distance “as the crow flies”), you follow the line segment joining them. But in real life this isn’t always possible. If you are driving your car through a city or across your campus, you need to go around solid objects and not through them. So how do we calculate distance in those cases? Measuring distance in a set X is a very small (but interesting) part of a branch of mathematics known as “point set topologyTopology,” and we will look at it in detail in this chapter.