Topologies On Closed And Closed Convex Sets
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Topologies On Closed And Closed Convex Sets
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Author : Gerald Beer
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-10-31
Topologies On Closed And Closed Convex Sets written by Gerald Beer 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 1993-10-31 with Mathematics categories.
This monograph provides an introduction to the theory of topologies defined on the closed subsets of a metric space, and on the closed convex subsets of a normed linear space as well. A unifying theme is the relationship between topology and set convergence on the one hand, and set functionals on the other. The text includes for the first time anywhere an exposition of three topologies that over the past ten years have become fundamental tools in optimization, one-sided analysis, convex analysis, and the theory of multifunctions: the Wijsman topology, the Attouch--Wets topology, and the slice topology. Particular attention is given to topologies on lower semicontinuous functions, especially lower semicontinuous convex functions, as associated with their epigraphs. The interplay between convex duality and topology is carefully considered and a chapter on set-valued functions is included. The book contains over 350 exercises and is suitable as a graduate text. This book is of interest to those working in general topology, set-valued analysis, geometric functional analysis, optimization, convex analysis and mathematical economics.
Convexity
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Author : Barry Simon
language : en
Publisher: Cambridge University Press
Release Date : 2011-05-19
Convexity written by Barry Simon 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 2011-05-19 with Mathematics categories.
Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces the reader to the basic definitions and ideas that play central roles throughout the book. The rest of the book is divided into four parts: convexity and topology on infinite-dimensional spaces; Loewner's theorem; extreme points of convex sets and related issues, including the Krein–Milman theorem and Choquet theory; and a discussion of convexity and inequalities. The connections between disparate topics are clearly explained, giving the reader a thorough understanding of how convexity is useful as an analytic tool. A final chapter overviews the subject's history and explores further some of the themes mentioned earlier. This is an excellent resource for anyone interested in this central topic.
Functional Analysis Sobolev Spaces And Partial Differential Equations
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Author : Haim Brezis
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-02
Functional Analysis Sobolev Spaces And Partial Differential Equations written by Haim Brezis 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 2010-11-02 with Mathematics categories.
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Infinite Dimensional Analysis
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Author : Charalambos D. Aliprantis
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-02
Infinite Dimensional Analysis written by Charalambos D. Aliprantis 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 2007-05-02 with Business & Economics categories.
This monograph presents a study of modern functional analysis. It is intended for the student or researcher who could benefit from functional analytic methods, but does not have an extensive background and does not plan to make a career as a functional analyst.
Modern Methods In Topological Vector Spaces
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Author : Albert Wilansky
language : en
Publisher: Courier Corporation
Release Date : 2013-01-01
Modern Methods In Topological Vector Spaces written by Albert Wilansky and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Mathematics categories.
"Designed for a one-year course in topological vector spaces, this text is geared toward beginning graduate students of mathematics. Topics include Banach space, open mapping and closed graph theorems, local convexity, duality, equicontinuity, operators,inductive limits, and compactness and barrelled spaces. Extensive tables cover theorems and counterexamples. Rich problem sections throughout the book. 1978 edition"--
Introduction To Banach Spaces And Their Geometry
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Author :
language : en
Publisher: Elsevier
Release Date : 2011-10-10
Introduction To Banach Spaces And Their Geometry written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-10 with Mathematics categories.
Introduction to Banach Spaces and their Geometry
Topological Vector Spaces And Distributions
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Author : John Horvath
language : en
Publisher: Courier Corporation
Release Date : 2013-10-03
Topological Vector Spaces And Distributions written by John Horvath and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-03 with Mathematics categories.
Precise exposition provides an excellent summary of the modern theory of locally convex spaces and develops the theory of distributions in terms of convolutions, tensor products, and Fourier transforms. 1966 edition.
Topological Vector Spaces And Their Applications
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Author : V.I. Bogachev
language : en
Publisher: Springer
Release Date : 2017-05-16
Topological Vector Spaces And Their Applications written by V.I. Bogachev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-16 with Mathematics categories.
This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. Overall, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.
Encyclopedia Of General Topology
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Author : K.P. Hart
language : en
Publisher: Elsevier
Release Date : 2003-11-18
Encyclopedia Of General Topology written by K.P. Hart and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-18 with Mathematics categories.
This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book.Key features:• More terms from General Topology than any other book ever published• Short and informative articles• Authors include the majority of top researchers in the field• Extensive indexing of terms
Dynamics Games And Science Ii
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Author : Mauricio Matos Peixoto
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-27
Dynamics Games And Science Ii written by Mauricio Matos Peixoto 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 2011-05-27 with Mathematics categories.
Dynamics, Games and Science I and II are a selection of surveys and research articles written by leading researchers in mathematics. The majority of the contributions are on dynamical systems and game theory, focusing either on fundamental and theoretical developments or on applications to modeling in biology, ecomonics, engineering, finances and psychology. The papers are based on talks given at the International Conference DYNA 2008, held in honor of Mauricio Peixoto and David Rand at the University of Braga, Portugal, on September 8-12, 2008. The aim of these volumes is to present cutting-edge research in these areas to encourage graduate students and researchers in mathematics and other fields to develop them further.