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Basic Topology 1 = Metric Spaces and General Topology /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Basic Topology 1/ 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.
面頁冊數:	XXVIII, 502 p. 17 illus., 6 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Analysis. -
電子資源:	https://doi.org/10.1007/978-981-16-6509-7
ISBN:	9789811665097

Basic Topology 1 = Metric Spaces and General Topology /
Adhikari, Avishek.

Basic Topology 1Metric Spaces and General Topology /[electronic resource] :by Avishek Adhikari, Mahima Ranjan Adhikari. - 1st ed. 2022. - XXVIII, 502 p. 17 illus., 6 illus. in color.online resource.

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

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

669490
Analysis.

LC Class. No.: QA611-614.97

Dewey Class. No.: 514

Basic Topology 1 = Metric Spaces and General Topology /
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