Notes on Topology

These are links to (mostly) PostScript files containing notes for various topics in topology. They were originally written back in the 1980's, then revised around 1999. Eventually I'd like to revise them, at which point they'll be available as web pages and PDF files like my other online notes.

I learned topology at M.I.T. from Topology: A First Course by James Munkres. At the time, the first edition was just coming out; I still have the photocopies we were given before the printed version was ready!

Hence, I'm a bit biased: I still think Munkres' book is the best book to learn from. The writing is clear and lively, the choice of topics is still pretty good, and the exercises are wonderful. Munkres also has a gift for naming things in useful ways (The Pasting Lemma, the Sequence Lemma, the Tube Lemma).

(I like Paul Halmos's suggestion that things be named in descriptive ways. On the other hand, some names in topology are terrible --- "first countable" and "second countable" come to mind. They are almost as bad as "regions of type I" and "regions of type II" which you still sometimes encounter in books on multivariable calculus.)

I've used Munkres both of the times I've taught topology, the most recent occasion being 1999. The lecture notes below follow the order of the topics in the book, with a few minor variations.

Here are some areas in which I decided to do things differently from Munkres:

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