Topology: A Categorical Approach 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024


Topology: A Categorical Approach

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Tai-Danae Bradley 作者
The MIT Press
譯者
2020-8-18 出版日期
168 頁數
USD 35.00 價格
Paperback
叢書系列
9780262539357 圖書編碼

Topology: A Categorical Approach 在線電子書 圖書標籤: 數學  拓撲學   


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Topology: A Categorical Approach 在線電子書 epub 下載 mobi 下載 pdf 下載 txt 下載 2024

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Topology: A Categorical Approach 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024



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Topology: A Categorical Approach 在線電子書 著者簡介

Tai-Danae Bradley is a PhD candidate in mathematics at the CUNY Graduate Center in New York. She is creator of the popular math blog, Math3ma and author of an open access ebook called "What Is Applied Category Theory?"

Tyler Bryson is a PhD student in mathematics at the CUNY Graduate Center in New York.

John Terilla is a mathematics professor at Queens College and the CUNY Graduate Center in New York. He advises Terilla and Bradley and conducts research in algebraic topology, quantum physics, and deformation theory.


Topology: A Categorical Approach 在線電子書 著者簡介


Topology: A Categorical Approach 在線電子書 pdf 下載 txt下載 epub 下載 mobi 在線電子書下載

Topology: A Categorical Approach 在線電子書 圖書描述

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.

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