[macosxnerd101]

The author also notes there are some errors in this draft, but I think it's still a good illustration of why CS folk might care about topology (not being a topology person, myself).

Quote

CS grad students often have to take classes in category theory. These classes always want to use groups and topological spaces as examples, and my experience is that at this point many of the students shift uncomfortably in their seats since they have not had undergraduate classes in group theory, topology, analysis, or anything else relevant. But you do not have to know much topology to be able to appreciate the example, so I tried to write up the minimal amount necessary. Similarly, if you already understand intuitionistic logic, you do not need to know much topology to understand the way in which topological spaces are natural models for intuitionistic logic—but you do need to know more than zero.

So a couple of years ago I wrote up a short introduction to topology for first-year computer science grad students and other people who similarly might like to know the absolute minimum, and only the absolute minimum, about topology. It came out somewhat longer than I expected, 11 pages, of which 6 are the introduction, and 5 are about typical applications to computer science. But it is a very light, fluffy 11 pages, and I am generally happy with it.

http://blog.plover.c...pology-doc.html