{"product_id":"topology-isbn-9780262539357","title":"Topology","description":"\u003cb\u003eA graduate-level textbook that presents basic topology from the perspective of category theory.\u003c\/b\u003e\u003cp\u003eThis 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. \u003c\/p\u003e\u003cp\u003eAfter 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.\u003cbr\u003e\u003c\/p\u003e0 Preliminaries\u003cbr\u003e1 Examples and Constructions\u003cbr\u003e2 Connectedness and Compactness\u003cbr\u003e3 Limits of Sequences and Filters\u003cbr\u003e4 Categorical Limits and Colimits\u003cbr\u003e5 Adjunctions and the Compact-Open Topology\u003cbr\u003e6 Paths, Loops, Cylinders, Suspensions, . . .\u003cbr\u003eGlossary of Symbols\u003cbr\u003eBibliography\u003cbr\u003eIndexTai-Danae Bradley is a PhD candidate in mathematics at the CUNY Graduate Center and the creator of the popular math blog, Math3ma.\u003cbr\u003e\u003cbr\u003eTyler Bryson is a PhD candidate in mathematics at the CUNY Graduate Center.\u003cbr\u003e\u003cbr\u003eJohn Terilla is Professor of Mathematics at Queens College and on the Doctoral Faculty at the CUNY Graduate Center.A graduate-level textbook that presents basic topology from the perspective of category theory.","brand":"The MIT Press","offers":[{"title":"Default Title","offer_id":46305420345573,"sku":"NP9780262539357","price":35.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780262539357.jpg?v=1767742827","url":"https:\/\/k12savings.com\/products\/topology-isbn-9780262539357","provider":"K12savings","version":"1.0","type":"link"}