COMPACT, a tutorial

Scott W. Williams

State University of New York in Buffalo

title and preface

page 1:
the beginnings

the universe in a box

page 2:
a special example

open covers

functional separation





I was invited to present a one hour tutorial on Topology for students attending the fifth annual Conference for African American Researchers in the Mathematical Sciences held June 22-26, 1999 at the University of Michigan - Ann Arbor. This is a world wide web version of my notes for the lecture and is presented in five parts.

When organizer Bill Massey heard the title of this lecture, he said jokingly, I hope you will not try to convince us that "the finite subcover" business is "natural." Well, I do not believe it is natural nor do I believe it is intuitive; on the other hand, I believe Topology was invented, in part, to focus upon a few ideas, one of which is compactness. In this tutorial, I will switch between the intuitive and the accurate, between historical motivations and modern interest.

Scott W. Williams