Basic topology. 1, Metric spaces and general topology / Avishek Adhikari, Mahima Ranjan Adhikari.
Adhikari, Avishek, 1983- author.; Adhikari, Mahima Ranjan, author.
2022
QA611
Available Online

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Title Basic topology. 1, Metric spaces and general topology / Avishek Adhikari, Mahima Ranjan Adhikari.
Author Adhikari, Avishek, 1983- author.
ISBN 9789811665097 (electronic bk.)
9811665095 (electronic bk.)
9789811665080
9811665087
DOI https://doi.org/10.1007/978-981-16-6509-7
Published Singapore : Springer, 2022.
Language English
Description 1 online resource : illustrations (black and white, and color).
Item Number 10.1007/978-981-16-6509-7 doi
Call Number QA611
Dewey Decimal Classification 514
Summary 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 StoneCech compactification and Alexandroff one-point compactification. This volume also includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and GelfandKolmogoroff 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 concepts leading 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.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Added Author Adhikari, Mahima Ranjan, author.
Available in Other Form Basic topology 1.
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1. Prerequisites: Sets, Algebraic Systems, and Classical Analysis
2. Metric Spaces and Normed Linear Spaces
3. Topological Spaces and Continuous Maps
4. Separation Axioms
5. Compactness and Connectedness
6. Real-valued Continuous Functions
7. Countability, Separability and Embedding
8. Brief History of General Topology.

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