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Basic topology.1,Metric spaces and general topology

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Basic topology.by Avishek Adhikari, Mahima Ranjan Adhikari.
其他題名:	Metric spaces and general topology
作者:	Adhikari, Avishek.
其他作者:	Adhikari, Mahima Ranjan.
出版者:	Singapore :Springer Nature Singapore :2022.
面頁冊數:	xxviii, 502 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Topology.
電子資源:	https://doi.org/10.1007/978-981-16-6509-7
ISBN:	9789811665097$q(electronic bk.)

Basic topology.1,Metric spaces and general topology
Adhikari, Avishek.

Basic topology.1,Metric spaces and general topology[electronic resource] /Metric spaces and general topologyby Avishek Adhikari, Mahima Ranjan Adhikari. - Singapore :Springer Nature Singapore :2022. - xxviii, 502 p. :ill., digital ;24 cm.

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.

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.

ISBN: 9789811665097$q(electronic bk.)

Standard No.: 10.1007/978-981-16-6509-7doiSubjects--Topical Terms:

185965
Topology.

LC Class. No.: QA611 / .A34 2022

Dewey Class. No.: 514

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520 $a 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.
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