Basic Topology 3
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Basic Topology 3
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Author : Mahima Ranjan Adhikari
language : en
Publisher:
Release Date : 2022
Basic Topology 3 written by Mahima Ranjan Adhikari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. 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 theory and applications in a balanced unified way.
Basic Topology
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Author : M.A. Armstrong
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Basic Topology written by M.A. Armstrong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.
In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for their calculating. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties help students gain a thorough understanding of the subject.
Basic Topology 3
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Author : Mahima Ranjan Adhikari
language : en
Publisher: Springer Nature
Release Date : 2023-03-15
Basic Topology 3 written by Mahima Ranjan Adhikari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-15 with Mathematics categories.
This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. 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 theory and applications in a balanced unified way.
Basic Topology 2
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Author : Avishek Adhikari
language : en
Publisher: Springer
Release Date : 2022-03-02
Basic Topology 2 written by Avishek Adhikari and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-02 with Mathematics categories.
This second of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, algebra, and the theory of numbers. Offering a proper background on topology, analysis, and algebra, this volume discusses the topological groups and topological vector spaces that provide many interesting geometrical objects which relate algebra with geometry and analysis. This volume follows a systematic and comprehensive elementary approach to the topology related to manifolds, emphasizing differential topology. It further communicates the history of the emergence of the concepts leading to the development of topological groups, manifolds, and also Lie groups as mathematical topics with their motivations. This book will promote the scope, power, and active learning of the subject while covering a wide range of theories and applications in a balanced unified way.
Recent Progress In General Topology Iii
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Author : K.P. Hart
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Recent Progress In General Topology Iii written by K.P. Hart and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.
Essential Topology
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Author : Martin D. Crossley
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-11
Essential Topology written by Martin D. Crossley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-11 with Mathematics categories.
This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra.
General Topology I
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Author : A.V. Arkhangel'skii
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
General Topology I written by A.V. Arkhangel'skii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is the first of the encyclopaedia volumes devoted to general topology. It has two parts. The first outlines the basic concepts and constructions of general topology, including several topics which have not previously been covered in English language texts. The second part presents a survey of dimension theory, from the very beginnings to the most important recent developments. The principal ideas and methods are treated in detail, and the main results are provided with sketches of proofs. The authors have suceeded admirably in the difficult task of writing a book which will not only be accessible to the general scientist and the undergraduate, but will also appeal to the professional mathematician. The authors' efforts to detail the relationship between more specialized topics and the central themes of topology give the book a broad scholarly appeal which far transcends narrow disciplinary lines.
Basic Topology 1
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Author : Avishek Adhikari
language : en
Publisher: Springer Nature
Release Date : 2022-07-04
Basic Topology 1 written by Avishek Adhikari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-04 with Mathematics categories.
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.
Basic Topology
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Author : Mark Anthony Armstrong
language : en
Publisher:
Release Date : 1990
Basic Topology written by Mark Anthony Armstrong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Basic Algebraic Topology And Its Applications
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Author : Mahima Ranjan Adhikari
language : en
Publisher: Springer
Release Date : 2016-09-16
Basic Algebraic Topology And Its Applications written by Mahima Ranjan Adhikari and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-16 with Mathematics categories.
This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.