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Topology
A Categorical Approach
Taschenbuch von Tai-Danae Bradley
Sprache: Englisch

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Beschreibung
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.

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.

Über den Autor
Tai-Danae Bradley, Tyler Bryson, and John Terilla
Inhaltsverzeichnis
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
Details
Erscheinungsjahr: 2020
Fachbereich: Topologie
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: Einband - flex.(Paperback)
ISBN-13: 9780262539357
ISBN-10: 0262539357
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Bradley, Tai-Danae
Hersteller: MIT Press Ltd
Verantwortliche Person für die EU: preigu, Ansas Meyer, Lengericher Landstr. 19, D-49078 Osnabrück, mail@preigu.de
Maße: 180 x 230 x 16 mm
Von/Mit: Tai-Danae Bradley
Erscheinungsdatum: 18.08.2020
Gewicht: 0,342 kg
Artikel-ID: 127473132
Über den Autor
Tai-Danae Bradley, Tyler Bryson, and John Terilla
Inhaltsverzeichnis
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
Details
Erscheinungsjahr: 2020
Fachbereich: Topologie
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: Einband - flex.(Paperback)
ISBN-13: 9780262539357
ISBN-10: 0262539357
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Bradley, Tai-Danae
Hersteller: MIT Press Ltd
Verantwortliche Person für die EU: preigu, Ansas Meyer, Lengericher Landstr. 19, D-49078 Osnabrück, mail@preigu.de
Maße: 180 x 230 x 16 mm
Von/Mit: Tai-Danae Bradley
Erscheinungsdatum: 18.08.2020
Gewicht: 0,342 kg
Artikel-ID: 127473132
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