Proximity Approach To Problems In Topology And Analysis
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Proximity Approach To Problems In Topology And Analysis
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Author : Somashekhar Naimpally
language : en
Publisher: Walter de Gruyter
Release Date : 2010-10-01
Proximity Approach To Problems In Topology And Analysis written by Somashekhar Naimpally and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-01 with Mathematics categories.
Dieses Buch konzentriert das aktuelle Gesamtwissen zum Proximity-Konzept und stellt es dem Leser in gut strukturierter Form dar. Hauptaugenmerk liegt auf den vielfältigen Möglichkeiten, die sich aus dem Proximity-Konzept der räumlichen Nähe und seiner Verallgemeinerung im Nearness-Konzept ergeben.
A User S Guide To Algebraic Topology
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Author : C. T. J. Dodson
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-01-31
A User S Guide To Algebraic Topology written by C. T. J. Dodson 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 1997-01-31 with Mathematics categories.
This book arose from courses taught by the authors, and is designed for both instructional and reference use during and after a first course in algebraic topology. It is a handbook for users who want to calculate, but whose main interests are in applications using the current literature, rather than in developing the theory. Typical areas of applications are differential geometry and theoretical physics. We start gently, with numerous pictures to illustrate the fundamental ideas and constructions in homotopy theory that are needed in later chapters. We show how to calculate homotopy groups, homology groups and cohomology rings of most of the major theories, exact homotopy sequences of fibrations, some important spectral sequences, and all the obstructions that we can compute from these. Our approach is to mix illustrative examples with those proofs that actually develop transferable calculational aids. We give extensive appendices with notes on background material, extensive tables of data, and a thorough index. Audience: Graduate students and professionals in mathematics and physics.
Topology With Applications
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Author : Somashekhar A. Naimpally
language : en
Publisher: World Scientific
Release Date : 2013
Topology With Applications written by Somashekhar A. Naimpally and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.
Bornologies And Lipschitz Analysis
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Author : Gerald Beer
language : en
Publisher: CRC Press
Release Date : 2023-05-15
Bornologies And Lipschitz Analysis written by Gerald Beer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-15 with Mathematics categories.
This monograph, for the first time in book form, considers the large structure of metric spaces as captured by bornologies: families of subsets that contain the singletons, that are stable under finite unions, and that are stable under taking subsets of its members. The largest bornology is the power set of the space and the smallest is the bornology of its finite subsets. Between these lie (among others) the metrically bounded subsets, the relatively compact subsets, the totally bounded subsets, and the Bourbaki bounded subsets. Classes of functions are intimately connected to various bornologies; e.g., (1) a function is locally Lipschitz if and only if its restriction to each relatively compact subset is Lipschitz; (2) a subset is Bourbaki bounded if and only if each uniformly continuous function on the space is bounded when restricted to the subset. A great deal of attention is given to the variational notions of strong uniform continuity and strong uniform convergence with respect to the members of a bornology, leading to the bornology of UC-subsets and UC-spaces. Spaces on which its uniformly continuous real-valued functions are stable under pointwise product are characterized in terms of the coincidence of the Bourbaki bounded subsets with a usually larger bornology. Special attention is given to Lipschitz and locally Lipschitz functions. For example, uniformly dense subclasses of locally Lipschitz functions within the real-valued continuous functions, Cauchy continuous functions, and uniformly continuous functions are presented. It is shown very generally that a function between metric spaces has a particular metric property if and only if whenever it is followed in a composition by a real-valued Lipschitz function, the composition has the property. Bornological convergence of nets of closed subsets, having Attouch-Wets convergence as a prototype, is considered in detail. Topologies of uniform convergence for continuous linear operators between normed spaces is explained in terms of the bornological convergence of their graphs. Finally, the idea of a bornological extension of a topological space is presented, and all regular extensions can be so realized.
Transactions On Rough Sets Xxi
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Author : James F. Peters
language : en
Publisher: Springer
Release Date : 2019-02-01
Transactions On Rough Sets Xxi written by James F. Peters and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-01 with Computers categories.
The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery, and intelligent information processing, to relations between rough sets and other approaches to uncertainty, vagueness, and incompleteness, such as fuzzy sets and theory of evidence. Volume XXI in the series is a continuation of a number of research streams that have grown out of the seminal work of Zdzislaw Pawlak during the first decade of the 21st century.
Transactions On Rough Sets Xvii
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Author : James F. Peters
language : en
Publisher: Springer
Release Date : 2014-03-03
Transactions On Rough Sets Xvii written by James F. Peters and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-03 with Computers categories.
The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery and intelligent information processing, to relations between rough sets and other approaches to uncertainty, vagueness, and incompleteness, such as fuzzy sets and theory of evidence. Volume XVII is a continuation of a number of research streams which have grown out of the seminal work by Zdzislaw Pawlak during the first decade of the 21st century. The research streams represented in the papers cover both theory and applications of rough, fuzzy and near sets as well as their combinations.
Integrated Computing Technology
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Author : Estevam Rafael Hruschka
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-24
Integrated Computing Technology written by Estevam Rafael Hruschka 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 2011-06-24 with Computers categories.
This book constitutes the refereed proceedings of the First International Conference on Integrated Computing Technology, INTECH 2011, held in Sao Carlos, Brazil, in May/ June 2011. The 14 revised full papers presented were carefully reviewed and selected from 103 submissions. The conference fosters discussions in integrating models, framework, designs, content,networks and the knowledge through more robust and high quality research.
Innovations In Intelligent Image Analysis
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Author : Halina Kwasnicka
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-17
Innovations In Intelligent Image Analysis written by Halina Kwasnicka 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 2011-02-17 with Computers categories.
This book presents an introduction to new and important research in the images processing and analysis area. It is hoped that this book will be useful for scientists and students involved in many aspects of image analysis. The book does not attempt to cover all of the aspects of Computer Vision, but the chapters do present some state of the art examples.
Beyond Topology
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Author : Frdric Mynard
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-05-15
Beyond Topology written by Frdric Mynard 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 2009-05-15 with Mathematics categories.
The purpose of this collection is to guide the non-specialist through the basic theory of various generalizations of topology, starting with clear motivations for their introduction. Structures considered include closure spaces, convergence spaces, proximity spaces, quasi-uniform spaces, merotopic spaces, nearness and filter spaces, semi-uniform convergence spaces, and approach spaces. Each chapter is self-contained and accessible to the graduate student, and focuses on motivations to introduce the generalization of topologies considered, presenting examples where desirable properties are not present in the realm of topologies and the problem is remedied in the more general context. Then, enough material will be covered to prepare the reader for more advanced papers on the topic. While category theory is not the focus of the book, it is a convenient language to study these structures and, while kept as a tool rather than an object of study, will be used throughout the book. For this reason, the book contains an introductory chapter on categorical topology.
General Topology And Its Relations To Modern Analysis And Algebra V
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Author : Josef Novák
language : en
Publisher:
Release Date : 1983
General Topology And Its Relations To Modern Analysis And Algebra V written by Josef Novák and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Algebra categories.