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＜電子ブック＞
Basic Topology 1 : Metric Spaces and General Topology / by Avishek Adhikari, Mahima Ranjan Adhikari

版	1st ed. 2022.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2022
大きさ	XXVIII, 502 p. 17 illus., 6 illus. in color : online resource
著者標目	*Adhikari, Avishek author Adhikari, Mahima Ranjan author SpringerLink (Online service)
件　名	LCSH:Topology LCSH:Mathematical analysis FREE:Topology FREE:Analysis
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-981-16-6509-7

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