國立虎尾科技大學 |

A basic course in topology

Record Type:	Language materials, printed : Monograph/item
Title/Author:	A basic course in topology/ by 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:	Algebraic Topology. -
Online resource:	https://doi.org/10.1007/978-3-662-70602-2
ISBN:	9783662706022

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

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

672209
Algebraic Topology.

LC Class. No.: QA611

Dewey Class. No.: 514

A basic course in topology
LDR:02370nam a2200349 a 4500 001 1161523
003 DE-He213
005 20250215115450.0
006 m d
007 cr nn 008maaau
008 251029s2025 gw s 0 eng d
020 $a 9783662706022 $q (electronic bk.)
020 $a 9783662706015 $q (paper)
024 7 $a 10.1007/978-3-662-70602-2 $2 doi
035 $a 978-3-662-70602-2
040 $a GP $c GP
041 1 $a eng $h ger
050 4 $a QA611
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 514 $2 23
090 $a QA611 $b .L383 2025
100 1 $a Laures, Gerd. $e author. $3 1257349
240 1 0 $a Grundkurs Topologie. $l English
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.
650 2 4 $a Algebraic Topology. $3 672209
650 1 4 $a Algebraic Geometry. $3 670184
650 0 $a Topology. $3 633483
700 1 $a Szymik, Markus. $e author. $3 1257350
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Compact textbooks in mathematics. $3 1069870
856 4 0 $u https://doi.org/10.1007/978-3-662-70602-2
950 $a Mathematics and Statistics (SpringerNature-11649)