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Short introduction to topology for people who don't really care about topology

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Octocat-spinner-32 NOTES
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Octocat-spinner-32 README
Octocat-spinner-32 topology.pdf
Octocat-spinner-32 topology.tex
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 (


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

Please do not distribute this draft after 15 December, 2010.  The most
recent version is available at .


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