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Basic Topology 1: Metric Spaces and General Topology
Paperback
ISBN13: 9789811665110
Publisher: Springer Nature
Published: Jul 5 2023
Pages: 502
Weight: 1.62
Height: 1.07 Width: 6.14 Depth: 9.21
Language: English
This first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of distance in the Euclidean space. The special structure of a metric space induces a topology that leads to many applications of topology in modern analysis and modern algebra, as shown in this volume. This volume also studies topological properties such as compactness and connectedness. Considering the importance of compactness in mathematics, this study covers the Stone-Cech compactification and Alexandroff one-point compactification. This volume also includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand-Kolmogoroff theorem.
The content of this volume is spread into eight chapters of which the last chapter conveys the history of metric spaces and the history of the emergence of the conceptsleading to the development of topology as a subject with their motivations with an emphasis on general topology. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power, and active learning of the subject, all the while covering a wide range of theories and applications in a balanced unified way.
1 different editions
Also available
Basic Topology 1: Metric Spaces and General Topology
Adhikari, Avishek
Adhikari, Mahima Ranjan
Hardcover
Also from
Adhikari, Avishek
Basic Topology 2: Topological Groups, Topology of Manifolds and Lie Groups
Adhikari, Avishek
Adhikari, Mahima Ranjan
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Basic Topology 1: Metric Spaces and General Topology
Adhikari, Avishek
Adhikari, Mahima Ranjan
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Basic Topology 2: Topological Groups, Topology of Manifolds and Lie Groups
Adhikari, Mahima Ranjan
Adhikari, Avishek
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