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OverviewA 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. Full Product DetailsAuthor: Tai-Danae Bradley , Tyler Bryson , John TerillaPublisher: MIT Press Ltd Imprint: MIT Press Weight: 0.368kg ISBN: 9780262539357ISBN 10: 0262539357 Pages: 168 Publication Date: 18 August 2020 Audience: College/higher education , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of Contents0 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 IndexReviewsAuthor InformationTai-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. Tab Content 6Author Website:Countries AvailableAll regions |
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