Description
A graduate-level textbook that presents basic topology from the perspective of category theory.
This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.
Table of Contents
0 Preliminaries
1 Examples and Constructions
2 Connectedness and Compactness
3 Limits of Sequences and Filters
4 Categorical Limits and Colimits
5 Adjunctions and the Compact-Open Topology
6 Paths, Loops, Cylinders, Suspensions, . . .
Glossary of Symbols
Bibliography
Index
