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Topology by Tai-Danae Bradley, Tyler Bryson and John Terilla

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Topology

A Categorical Approach

A Categorical Approach

By Tai-Danae Bradley, Tyler Bryson and John Terilla

By Tai-Danae Bradley, Tyler Bryson and John Terilla

By Tai-Danae Bradley, Tyler Bryson and John Terilla

By Tai-Danae Bradley, Tyler Bryson and John Terilla

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Category: Nonfiction

Category: Nonfiction

Paperback $35.00

Aug 18, 2020 | ISBN 9780262539357

Ebook $25.99

Aug 18, 2020 | ISBN 9780262359627

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    Topology by Tai-Danae Bradley, Tyler Bryson and John Terilla
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    About Topology

    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.

    After presenting the basics of both category theory and topology, the book covers the universal properties of familiar constructions and three main topological properties—connectedness, Hausdorff, and compactness. It presents a fine-grained approach to convergence of sequences and filters; explores categorical limits and colimits, with examples; looks in detail at adjunctions in topology, particularly in mapping spaces; and examines additional adjunctions, presenting ideas from homotopy theory, the fundamental groupoid, and the Seifert van Kampen theorem. End-of-chapter exercises allow students to apply what they have learned. The book expertly guides students of topology through the important transition from undergraduate student with a solid background in analysis or point-set topology to graduate student preparing to work on contemporary problems in mathematics.

    About Topology

    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.

    Product Details

    Category: Nonfiction

    Paperback | $35.00
    Published by The MIT Press
    Aug 18, 2020 | 166 Pages | 7 x 9 | ISBN 9780262539357

    Category: Nonfiction

    Ebook | $25.99
    Published by The MIT Press
    Aug 18, 2020 | 166 Pages | 7 x 9 | ISBN 9780262359627

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    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

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