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 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.
General
| Imprint: |
Springer Verlag, Singapore
|
| Country of origin: |
Singapore |
| Release date: |
July 2023 |
| First published: |
2022 |
| Authors: |
Avishek Adhikari
• Mahima Ranjan Adhikari
|
| Dimensions: |
235 x 155mm (L x W) |
| Pages: |
502 |
| Edition: |
1st ed. 2022 |
| ISBN-13: |
978-981-16-6511-0 |
| Categories: |
Books
Promotions
|
| LSN: |
981-16-6511-7 |
| Barcode: |
9789811665110 |
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