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A basic course in topology

Record Type:	Electronic resources : 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.
[NT 15003449]:	- 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.
Contained By:	Springer Nature eBook
Subject:	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:

522026
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.
650 0 $a Topology. $3 522026
650 1 4 $a Algebraic Geometry. $3 893861
650 2 4 $a Algebraic Topology. $3 891269
700 1 $a Szymik, Markus. $3 3782669
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Compact textbooks in mathematics. $3 2107015
856 4 0 $u https://doi.org/10.1007/978-3-662-70602-2
950 $a Mathematics and Statistics (SpringerNature-11649)