Elements Of Point Set Topology
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Elements Of Point Set Topology
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Author : John D. Baum
language : en
Publisher: Courier Corporation
Release Date : 1991-01-01
Elements Of Point Set Topology written by John D. Baum and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-01 with Mathematics categories.
Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.
Elements Of Topology
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Author : Tej Bahadur Singh
language : en
Publisher: CRC Press
Release Date : 2013-05-20
Elements Of Topology written by Tej Bahadur Singh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-20 with Mathematics categories.
Topology is a large subject with many branches broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad variety of mathematical disciplines. Algebraic topology serves as a powerful tool for studying the problems in geometry and numerous other areas of mathematics. Ele
Non Hausdorff Topology And Domain Theory
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Author : Jean Goubault-Larrecq
language : en
Publisher: Cambridge University Press
Release Date : 2013-03-28
Non Hausdorff Topology And Domain Theory written by Jean Goubault-Larrecq and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-28 with Computers categories.
Introduces the basic concepts of topology with an emphasis on non-Hausdorff topology, which is crucial for theoretical computer science.
Elementary Topology
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Author : O. I͡A. Viro
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Elementary Topology written by O. I͡A. Viro and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
"This textbook on elementary topologycontains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elernentary segment centered at the notions of fundamental group and covering space. The reader who has mastered the core material acquires a strong background in elementary topology and will feel at home in the environment of abstract mathemeatics."--BOOK JACKET.
The Elements Of Operator Theory
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Author : Carlos S. Kubrusly
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-01
The Elements Of Operator Theory written by Carlos S. Kubrusly 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 2011-03-01 with Mathematics categories.
This second edition of Elements of Operator Theory is a concept-driven textbook that includes a significant expansion of the problems and solutions used to illustrate the principles of operator theory. Written in a user-friendly, motivating style intended to avoid the formula-computational approach, fundamental topics are presented in a systematic fashion, i.e., set theory, algebraic structures, topological structures, Banach spaces, and Hilbert spaces, culminating with the Spectral Theorem. Included in this edition: more than 150 examples, with several interesting counterexamples that demonstrate the frontiers of important theorems, as many as 300 fully rigorous proofs, specially tailored to the presentation, 300 problems, many with hints, and an additional 20 pages of problems for the second edition. *This self-contained work is an excellent text for the classroom as well as a self-study resource for researchers.
A Course In Point Set Topology
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Author : John B. Conway
language : en
Publisher: Springer
Release Date : 2016-08-23
A Course In Point Set Topology written by John B. Conway and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-23 with Mathematics categories.
This textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs. Prerequisites include calculus and at least one semester of analysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other topological notions in the real line. Appendices are included to bridge the gap between this new material and material found in an analysis course. Metric spaces are one of the more prevalent topological spaces used in other areas and are therefore introduced in the first chapter and emphasized throughout the text. This also conforms to the approach of the book to start with the particular and work toward the more general. Chapter 2 defines and develops abstract topological spaces, with metric spaces as the source of inspiration, and with a focus on Hausdorff spaces. The final chapter concentrates on continuous real-valued functions, culminating in a development of paracompact spaces.
Elements Of The Topology Of Plane Sets Of Points
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Author : Maxwell Herman Alexander Newman
language : en
Publisher: Praeger
Release Date : 1985-09-12
Elements Of The Topology Of Plane Sets Of Points written by Maxwell Herman Alexander Newman and has been published by Praeger this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-09-12 with Mathematics categories.
This book provides an elementary introduction to the ideas and methods of topology by the detailed study of certain topics. There are elegant but rigorous proofs of many of the basic theorems, and special attention is given to the results needed in the theory of functions.
Point Set Topology With Topics Basic General Topology For Graduate Studies
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Author : Robert Andre
language : en
Publisher: World Scientific
Release Date : 2024-01-19
Point Set Topology With Topics Basic General Topology For Graduate Studies written by Robert Andre and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-19 with Mathematics categories.
This textbook can be used as introduction to a general topology course at undergraduate and graduate level courses. However, many parts of this book present topological concepts that apply directly to functional analysis, which will be of interest to scholars working in those fields.In Part I, readers are eased into the main subject matter of general topology, being presented with summaries of normed vector spaces and metric spaces. Parts II to VI form the core material contained in most Basic General Topology courses. After having worked through the most fundamental concepts of topology, the reader will be exposed to brief introductions to more specialized or advanced topics of pointset topology. These are presented in Part VII in the form of a sequence of chapters, many of which can be read or studied independently or in short sequences of two or three chapters, provided that the student has mastered the previous sections.Chapters related to the more basic ideas of general topology are followed by a collection of 'concept review' questions, the answers to which are found in the main body of the text. These questions highlight the main concepts presented in that chapter, as well as ideas that are often overlooked when first encountered, which will help to test the students' understanding. The efforts required in answering correctly such questions will provide the student with the ability to solve more complex problems in the exercises collected at the end of each section.
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 calculating them. 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 will help students gain a rounded understanding of the subject.
Topology Of Surfaces
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Author : L.Christine Kinsey
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-09-26
Topology Of Surfaces written by L.Christine Kinsey 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 1997-09-26 with Mathematics categories.
" . . . that famous pedagogical method whereby one begins with the general and proceeds to the particular only after the student is too confused to understand even that anymore. " Michael Spivak This text was written as an antidote to topology courses such as Spivak It is meant to provide the student with an experience in geomet describes. ric topology. Traditionally, the only topology an undergraduate might see is point-set topology at a fairly abstract level. The next course the average stu dent would take would be a graduate course in algebraic topology, and such courses are commonly very homological in nature, providing quick access to current research, but not developing any intuition or geometric sense. I have tried in this text to provide the undergraduate with a pragmatic introduction to the field, including a sampling from point-set, geometric, and algebraic topology, and trying not to include anything that the student cannot immediately experience. The exercises are to be considered as an in tegral part of the text and, ideally, should be addressed when they are met, rather than at the end of a block of material. Many of them are quite easy and are intended to give the student practice working with the definitions and digesting the current topic before proceeding. The appendix provides a brief survey of the group theory needed.