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A basic course in topology

Record Type:	Electronic resources : Monograph/item
Title/Author:	A basic course in topologyby Gerd Laures, Markus Szymik.
Author:	Laures, Gerd.
other author:	Szymik, Markus.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg :2025.
Description:	xii, 245 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Topology.
Online resource:	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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245 1 2 $a A basic course in topology $h [electronic resource] / $c by Gerd Laures, Markus Szymik.
260 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Birkhäuser, $c 2025.
300 $a xii, 245 p. : $b ill., digital ; $c 24 cm.
490 1 $a Compact textbooks in mathematics, $x 2296-455X
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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650 1 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Algebraic Topology. $3 273784
700 1 $a Szymik, Markus. $3 993154
710 2 $a SpringerLink (Online service) $3 273601
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950 $a Mathematics and Statistics (SpringerNature-11649)