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Basic Topology 1

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Basic Topology 1

Avishek Adhikari, Mahima Ranjan Adhikari (Broschiert, Englisch)

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Beschreibung
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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Technische Daten

Erscheinungsdatum
05.07.2023
Sprache
Englisch
EAN
9789811665110
Herausgeber
Springer Singapore
Sonderedition
Nein
Autor
Avishek Adhikari, Mahima Ranjan Adhikari
Seitenanzahl
502
Einbandart
Broschiert
Buch Untertitel
Metric Spaces and General Topology
Autorenporträt
AVISHEK ADHIKARI, Ph.D., M.Sc. (Gold Medalist), is Professor at the Department of Mathematics, Presidency University, Kolkata, India. A recipient of the President of India Medal, ISCA Young Scientist Award, and the NANUM Fund by International Mathematical Union, Professor Adhikari did his Ph.D. from the Indian Statistical Institute, India, under the guidance of Professor Bimal Roy, the former Director of the Indian Statistical Institute. Earlier, Professor Adhikari was a faculty member at the Department of Pure Mathematics, University of Calcutta, Kolkata, from July 2006–January 2019. He is the founder Secretary of the Institute for Mathematics, Bioinformatics, Information Technology & Computer Science (IMBIC), India, having branches in Sweden and Japan, and the Treasurer of the Cryptology Research Society of India. He was the former Eastern Zonal coordinator of the M.Sc. and Ph.D. scholarship examinations by the National Board of Higher Mathematics (NBHM). He was a Post-Doctoral fellow at INRIA-Rocquencourt, France, and Visiting Scientist at Linkoping University, Sweden; Indian Statistical Institute, Kolkata. Professor Adhikari delivered invited talks at various universities and institutions abroad.
Schlagwörter
metric spaces, compactness, connectedness, topological groups, normed linear spaces, vector field, topological vector spaces, countability, separability, embedding
Thema-Inhalt
PBP - Topologie PBK - Mathematische Analysis, allgemein
Höhe
235 mm
Breite
15.5 cm

Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH

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