Short Introduction to Topology

(For Computer Science Grad Students)

(and other people who don't give a crap about topology

DRAFT version 0.6

Mark Jason Dominus (mjd@plover.com)

==WARNING==

This document is a draft, circulated only to attract comment and correction. It contains numerous errors of fact, vague overgeneralizations, and misleading implications. Many claims about general topological spaces in fact apply only to Hausdorff spaces. Much of the Applications section should be considered placeholders that bear only a vague resemblance to the correct, accurate explanations. Readers not already familiar with topology may come away with severe misapprehensions. Do not rely on it for anything.

Please send comments, suggestions, and corrections to the author at mjd@plover.com.

Please do not distribute this draft after 15 December, 2010. The most recent version is available at http://blog.plover.com/math/topology-doc.html .

==WHAT==

Topology is the branch of mathematics that tries to understand continuity and continuous functions. You probably don't need to know much topology for your CS degree, but people will bring it up from time to time. For example, you will hear in your category theory class that topological spaces form a category with continuous functions as the arrows. Or you will hear that certain topological spaces are natural models for intuitionistic logic. The goal of these notes is to be the minimal explanation of topology that will enable you to understand those two things.

==THANKS==

Thanks to Brent Yorgey, David Radcliffe, Robin Houston, Miles Gould, and Géry Debongnie for corrections.