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Basic Topology 1

- Metric Spaces and General Topology
Af: Mahima Ranjan Adhikari, Avishek Adhikari Engelsk Paperback

Basic Topology 1

- Metric Spaces and General Topology
Af: Mahima Ranjan Adhikari, Avishek Adhikari Engelsk Paperback
Tjek vores konkurrenters priser
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.
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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.
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Produktdetaljer
Sprog: Engelsk
Sider: 502
ISBN-13: 9789811665110
Indbinding: Paperback
Udgave:
ISBN-10: 9811665117
Kategori: Regning og matematisk analyse
Udg. Dato: 5 jul 2023
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer Verlag, Singapore
Oplagsdato: 5 jul 2023
Forfatter(e): Mahima Ranjan Adhikari, Avishek Adhikari
Forfatter(e) Mahima Ranjan Adhikari, Avishek Adhikari

Kategori Regning og matematisk analyse

ISBN-13 9789811665110

Sprog Engelsk

Indbinding Paperback

Sider 502

Udgave

Længde 0mm

Bredde 155mm

Højde 235mm

Udg. Dato 5 jul 2023

Oplagsdato 5 jul 2023

Forlag Springer Verlag, Singapore