A Taste of Topology

This should be a revelation for mathematics undergraduates. Having evolved from Rundes notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology, as well as some algebraic topology. It is accessible to undergraduates from the second year on, and even beginning graduate students can benefit from some sections. The well-chosen selection of examples is accessible to students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In places, Rundes text treats its material differently to other books on the subject, providing a fresh perspective. For example, Baires theorem is derived from Bourbakis Mittag-Leffler theorem; nets are used extensively, in particular for an intuitive proof of Tychonoffs theorem; and a short and elegant, but little known proof for the Stone-Weierstrass theorem is given.