### General Topology Notes

#### Posted by Tom Leinster

This semester, I’ve had the pleasure of teaching a 4th year undergraduate course on topology. One of the great things about it has been the students, who are a really engaged and gifted bunch. I’ve possibly enjoyed teaching this course more than any I’ve taught before.

Another pleasure is that, having nearly reached the end of term, I find that I’ve written a complete set of notes for the course. (There’s also an introductory lecture and a set of problem sheets.) Comments welcome! It’s the first year I’ve taught this, so presumably I’ll be using some version of these notes for the next couple of years.

The course begins with the definition of topological space and takes it from there, going through standard constructions and then compactness and connectedness. It seems to me that Year 4 is pretty late to be teaching this stuff (though Scottish university students typically start a year younger than those in England or Wales, so it’s roughly equivalent to 3rd year south of the border). But on the plus side, the students had already done a good amount on metric spaces, including compactness and connectedness, and that softened up the ground nicely.

Posted at November 19, 2014 10:45 AM UTC
## Re: General Topology Notes

I can’t help but notice that the parts of

Definition A2.1have names that look like the names of separation axioms.Whether the separation axioms

shouldhave names T$_k$ is of course debatable (they’re mostly indexed by lifting problems which of course need not be totally ordered at all — there was a paper on that arXiv’d sometime this year, but I can’t find it now).