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A basic course in topology

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A basic course in topologyby Gerd Laures, Markus Szymik.
作者:	Laures, Gerd.
其他作者:	Szymik, Markus.
出版者:	Berlin, Heidelberg :Springer Berlin Heidelberg :2025.
面頁冊數:	xii, 245 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Topology.
電子資源:	https://doi.org/10.1007/978-3-662-70602-2
ISBN:	9783662706022$q(electronic bk.)

A basic course in topology
Laures, Gerd.

A basic course in topology[electronic resource] /by Gerd Laures, Markus Szymik. - Berlin, Heidelberg :Springer Berlin Heidelberg :2025. - xii, 245 p. :ill., digital ;24 cm. - Compact textbooks in mathematics,2296-455X. - Compact textbooks in mathematics..

- Basic Concepts of Topology -- Universal Constructions -- Connectivity and Separation -- Compactness and Mapping Spaces -- Transformation Groups -- Paths and Loops -- The Fundamental Group -- Covering Spaces -- Bundles and Fibrations -- Sheaves -- Simplicial Sets.

This book serves as an introduction to topology, a branch of mathematics that studies the qualitative properties of geometric objects. It is designed as a bridge between elementary courses in analysis and linear algebra and more advanced classes in algebraic and geometric topology, making it particularly suitable for both undergraduate and graduate mathematics students. Additionally, it can be used for self-study. The authors employ the modern language of category theory to unify and clarify the concepts presented, with definitions supported by numerous examples and illustrations. The book includes over 170 exercises that reinforce and deepen the understanding of the material. Many sections feature brief insights into advanced topics, providing a foundation for study projects or seminar presentations. In addition to set-theoretic topology, the book covers essential concepts such as fundamental groups, covering spaces, bundles, sheaves, and simplicial methods, which are vital in contemporary geometry and topology.

ISBN: 9783662706022$q(electronic bk.)

Standard No.: 10.1007/978-3-662-70602-2doiSubjects--Topical Terms:

185965
Topology.

LC Class. No.: QA611

Dewey Class. No.: 514

A basic course in topology
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505 0 $a - Basic Concepts of Topology -- Universal Constructions -- Connectivity and Separation -- Compactness and Mapping Spaces -- Transformation Groups -- Paths and Loops -- The Fundamental Group -- Covering Spaces -- Bundles and Fibrations -- Sheaves -- Simplicial Sets.
520 $a This book serves as an introduction to topology, a branch of mathematics that studies the qualitative properties of geometric objects. It is designed as a bridge between elementary courses in analysis and linear algebra and more advanced classes in algebraic and geometric topology, making it particularly suitable for both undergraduate and graduate mathematics students. Additionally, it can be used for self-study. The authors employ the modern language of category theory to unify and clarify the concepts presented, with definitions supported by numerous examples and illustrations. The book includes over 170 exercises that reinforce and deepen the understanding of the material. Many sections feature brief insights into advanced topics, providing a foundation for study projects or seminar presentations. In addition to set-theoretic topology, the book covers essential concepts such as fundamental groups, covering spaces, bundles, sheaves, and simplicial methods, which are vital in contemporary geometry and topology.
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