Inside, you'll find a presentation of basic, point-set topology from the perspective of category theory, targeted at graduate students in a first-semester course on topology. The idea is that most of these students are already somewhat familiar with the point-set ideas through a course on analysis or undergraduate topology. For this reason, many graduate-level instructors are tempted to rush through point-set topology or to skip it altogether to reach algebraic topology, which can be more fun to learn and to teach.
Our book presents an alternative to this approach. Rather than skipping over the basic ideas, we view this as an excellent opportunity to introduce students to the modern viewpoint of category theory.