A Basic Course in Topology / by Gerd Laures, Markus Szymik.

Format:

Book

Author/Creator:

Laures, Gerd.

Contributor:

Szymik, Markus.

Series:

Compact Textbooks in Mathematics, 2296-455X

Language:

English

Subjects (All):

Geometry, Algebraic.

Algebraic topology.

Algebraic Geometry.

Algebraic Topology.

Local Subjects:

Algebraic Geometry.

Algebraic Topology.

Physical Description:

1 online resource (355 pages)

Edition:

1st ed. 2025.

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Birkhäuser, 2025.

Summary:

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.

Contents:

- 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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783662706022

3662706024

OCLC:

1500762175