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Catalogue Information
Field name	Details
Dewey Class	514
Title	Basic Topology 1 ( EBook) : Metric Spaces and General Topology / / by Avishek Adhikari, Mahima Ranjan Adhikari.
Author	Adhikari, Avishek
Added Personal Name	Adhikari, Mahima Ranjan
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2022.
Publication	Singapore : : Springer Nature Singapore : : Imprint: Springer, , 2022.
Physical Details	XXVIII, 502 p. 17 illus., 6 illus. in color. : online resource.
ISBN	9789811665097
Summary Note	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.:
Contents note	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.
Mode of acces to digital resource	Digital reproduction.-
	Cham :
	Springer International Publishing,
	2022. -
	Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-981-16-6509-7
Links to Related Works	Subject References: Analysis . Mathematical analysis . Topology . Authors: Adhikari, Avishek . Adhikari, Mahima Ranjan . author . Corporate Authors: SpringerLink (Online service) . Classification: 514 .

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Basic Topology 1: Metric Spaces and General Topology /

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