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Details
Title
Topology : an invitation / K. Parthasarathy.
Author
Parthasarathy, K., author.
ISBN
9789811694844 (electronic bk.)
9811694842 (electronic bk.)
9811694834
9789811694837
9811694842 (electronic bk.)
9811694834
9789811694837
Published
Singapore : Springer, [2022]
Copyright
©2022
Language
English
Description
1 online resource : illustrations.
Item Number
10.1007/978-981-16-9484-4 doi
Call Number
QA611
Dewey Decimal Classification
514
Summary
This book starts with a discussion of the classical intermediate value theorem and some of its uncommon "topological" consequences as an appetizer to whet the interest of the reader. It is a concise introduction to topology with a tinge of historical perspective, as the authors perception is that learning mathematics should be spiced up with a dash of historical development. All the basics of general topology that a student of mathematics would need are discussed, and glimpses of the beginnings of algebraic and combinatorial methods in topology are provided. All the standard material on basic set topology is presented, with the treatment being sometimes new. This is followed by some of the classical, important topological results on Euclidean spaces (the higher-dimensional intermediate value theorem of PoincareMiranda, Brouwers fixed-point theorem, the no-retract theorem, theorems on invariance of domain and dimension, Borsuks antipodal theorem, the BorsukUlam theorem and the LusternikSchnirelmannBorsuk theorem), all proved by combinatorial methods. This material is not usually found in introductory books on topology. The book concludes with an introduction to homotopy, fundamental groups and covering spaces. Throughout, original formulations of concepts and major results are provided, along with English translations. Brief accounts of historical developments and biographical sketches of the dramatis personae are provided. Problem solving being an indispensable process of learning, plenty of exercises are provided to hone the reader's mathematical skills. The book would be suitable for a first course in topology and also as a source for self-study for someone desirous of learning the subject. Familiarity with elementary real analysis and some felicity with the language of set theory and abstract mathematical reasoning would be adequate prerequisites for an intelligent study of the book.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Unitext ; 134.
Unitext. Matematica per il 3+2.
Unitext. Matematica per il 3+2.
Available in Other Form
TOPOLOGY.
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Table of Contents
1 Aperitif: The Intermediate Value Theorem
2 Metric spaces
3 Topological spaces
4 Continuous maps
5 Compact spaces
6Topologies dened by maps
7 Products of compact spaces
8 Separation axioms
9 Connected spaces
10 Countability axioms.
2 Metric spaces
3 Topological spaces
4 Continuous maps
5 Compact spaces
6Topologies dened by maps
7 Products of compact spaces
8 Separation axioms
9 Connected spaces
10 Countability axioms.