Topology

A Categorical Approach

Tai-Danae Bradley, Tyler Bryson, John Terilla

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English

MIT Press
17 November 2020

Mathematics & Sciences; Topology

A graduate-level textbook that presents basic topology from the perspective of category theory.

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.

By: Tai-Danae Bradley, Tyler Bryson, John Terilla
Imprint: MIT Press
Country of Publication: United States
Dimensions: Height: 229mm, Width: 178mm,
Weight: 368g
ISBN: 9780262539357
ISBN 10: 0262539357
Pages: 168
Publication Date: 17 November 2020
Audience: College/higher education , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Tai-Danae Bradley is a PhD candidate in mathematics at the CUNY Graduate Center and the creator of the popular math blog, Math3ma. Tyler Bryson is a PhD candidate in mathematics at the CUNY Graduate Center. John Terilla is Professor of Mathematics at Queens College and on the Doctoral Faculty at the CUNY Graduate Center.