An Introduction To Inverse Limits With Set Valued Functions

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An Introduction To Inverse Limits With Set Valued Functions

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Author : W.T. Ingram
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-11

An Introduction To Inverse Limits With Set Valued Functions written by W.T. Ingram 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 2012-08-11 with Mathematics categories.

Inverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical systems and economics. This brief provides a concise introduction dedicated specifically to such inverse limits. The theory is presented along with detailed examples which form the distinguishing feature of this work. The major differences between the theory of inverse limits with mappings and the theory with set-valued functions are featured prominently in this book in a positive light. The reader is assumed to have taken a senior level course in analysis and a basic course in topology. Advanced undergraduate and graduate students, and researchers working in this area will find this brief useful. ​

Inverse Limits

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Author : W.T. Ingram
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-06

Inverse Limits written by W.T. Ingram 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 2011-11-06 with Mathematics categories.

Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introduction through inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influence of dynamics can be seen throughout; for instance, it includes studies of inverse limits with maps from families of maps that are of interest to dynamicists such as the logistic and the tent families. This book will serve as a useful reference to graduate students and researchers in continuum theory and dynamical systems. Researchers working in applied areas who are discovering inverse limits in their work will also benefit from this book.

Topics On Continua

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Author : Sergio Macías
language : en
Publisher: Springer
Release Date : 2018-07-24

Topics On Continua written by Sergio Macías and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-24 with Mathematics categories.

This book is a significant companion text to the existing literature on continuum theory. It opens with background information of continuum theory, so often missing from the preceding publications, and then explores the following topics: inverse limits, the Jones set function T, homogenous continua, and n-fold hyperspaces. In this new edition of the book, the author builds on the aforementioned topics, including the unprecedented presentation of n-fold hyperspace suspensions and induced maps on n-fold hyperspaces. The first edition of the book has had a remarkable impact on the continuum theory community. After twelve years, this updated version will also prove to be an excellent resource within the field of topology.

Set Valued Convex And Nonsmooth Analysis In Dynamics And Control

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Author : Rafal K. Goebel
language : en
Publisher: SIAM
Release Date : 2024-06-26

Set Valued Convex And Nonsmooth Analysis In Dynamics And Control written by Rafal K. Goebel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-26 with Mathematics categories.

Set-valued analysis, convex analysis, and nonsmooth analysis are relatively modern branches of mathematical analysis that have become increasingly relevant in current control theory and control engineering literature. This book serves as a broad introduction to analytical tools in these fields and to their applications in dynamical and control systems and is the first to cover these topics with this scope and at this level. Both continuous-time and discrete-time mutlivalued dynamics, modeled by differential and difference inclusions, are considered. Set-Valued, Convex, and Nonsmooth Analysis in Dynamics and Control: An Introduction is aimed at graduate students in control engineering and applied mathematics and researchers in control engineering who have no prior exposure to set-valued, convex, and nonsmooth analysis. The book will also be of interest to advanced undergraduate mathematics students and mathematicians with no prior exposure to the topic. The expected mathematical background is a course on nonlinear differential equations / dynamical systems and a course on real analysis. Knowledge of some control theory is helpful, but not essential.

Topology

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Author : K. Kuratowski
language : en
Publisher: Elsevier
Release Date : 2014-05-12

Topology written by K. Kuratowski and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.

Topology, Volume I deals with topology and covers topics ranging from operations in logic and set theory to Cartesian products, mappings, and orderings. Cardinal and ordinal numbers are also discussed, along with topological, metric, and complete spaces. Great use is made of closure algebra. Comprised of three chapters, this volume begins with a discussion on general topological spaces as well as their specialized aspects, including regular, completely regular, and normal spaces. Fundamental notions such as base, subbase, cover, and continuous mapping, are considered, together with operations such as the exponential topology and quotient topology. The next chapter is devoted to the study of metric spaces, starting with more general spaces, having the limit as its primitive notion. The space is assumed to be metric separable, and this includes problems of cardinality and dimension. Dimension theory and the theory of Borei sets, Baire functions, and related topics are also discussed. The final chapter is about complete spaces and includes problems of general function theory which can be expressed in topological terms. The book includes two appendices, one on applications of topology to mathematical logics and another to functional analysis. This monograph will be helpful to students and practitioners of algebra and mathematics.

Fungsi Bernilai Himpunan

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Author : Mohamad Muslikh
language : id
Publisher: Universitas Brawijaya Press
Release Date : 2022-11-30

Fungsi Bernilai Himpunan written by Mohamad Muslikh and has been published by Universitas Brawijaya Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-30 with Mathematics categories.

Buku ini mengenalkan kepada pembaca tentang fungsi bernilai himpunan (set-valued function). Fungsi bernilai himpunan kadang kala dalam literatur disebut dengan Correspondences atau Multifunction. Fungsi dalam kalkulus yang banyak dijumpai dalam materi pelajaran di sekolah menengah hingga perguruan tinggi dalam konteks ini, disebut fungsi bernilai tunggal atau singleton (himpunan yang anggotanya tunggal) sehingga fungsi bernilai himpunan dapat dikatakan sebagai generalisasi fungsi bernilai tunggal. Buku ini memberikan gambaran peranan fungsi bemilai himpunan pada bidang ilmu lain. Sebagaimana fungsi bernilai tunggal, dalam buku ini disajikan pengertian fungsi bernilai himpunan, operasinya, limit dan kekontinuannya. Pengertian jarak dua himpunan yang melandasi pembahasan kekontinuan juga diuraikan secara detail. Pengertian titik tetap untuk fungsi bernilai himpunan disajikan secara konstruktif demikian juga fungsi seleksi, yaitu fungsi bernilai tunggal yang merupakan anggota fungsi bernilai himpunan. Teknik seleksi ini seperti aksioma pilihan (axiom of choice). Pada dua bab terakhir disajikan penggunaan fungsi bernilai himpunan dalam bidang ekonomi. Karakteristik konsumen dan keseimbangan harga Walras dalam peristiwa pertukaran ekonorni dibahas secara teoretis dan diberikan contoh-contoh yang memadai dalam buku ini.

Set Valued Analysis

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Author : Jean-Pierre Aubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-02

Set Valued Analysis written by Jean-Pierre Aubin 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 2009-03-02 with Science categories.

"An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the near-impossible—it has made a subject which is generally inhospitable to nonspecialists because of its ‘family jargon’ appear nonintimidating even to a beginning graduate student." —The Journal of the Indian Institute of Science "The book under review gives a comprehensive treatment of basically everything in mathematics that can be named multivalued/set-valued analysis. ...The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of set-valued analysis." —Mathematical Reviews "This book provides a thorough introduction to multivalued or set-valued analysis... The style is lively and vigorous, the relevant historical comments and suggestive overviews increase the interest for this work...Graduate students and mathematicians of every persuasion will welcome this unparalleled guide to set-valued analysis." —Zentralblatt Math

Optima And Equilibria

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Author : Jean-Pierre Aubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Optima And Equilibria written by Jean-Pierre Aubin 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 2013-03-09 with Mathematics categories.

Progress in the theory of economic equilibria and in game theory has proceeded hand in hand with that of the mathematical tools used in the field, namely nonlinear analysis and, in particular, convex analysis. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its application to economics, has written a rigorous and concise - yet still elementary and self-contained - textbook providing the mathematical tools needed to study optima and equilibria, as solutions to problems, arising in economics, management sciences, operations research, cooperative and non-cooperative games, fuzzy games etc. It begins with the foundations of optimization theory, and mathematical programming, and in particular convex and nonsmooth analysis. Nonlinear analysis is then presented, first game-theoretically, then in the framework of set valued analysis. These results are then applied to the main classes of economic equilibria. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses.

Inverse Limits Of Set Valued Functions

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Author : Alexander Nelson Cornelius
language : en
Publisher:
Release Date : 2009

Inverse Limits Of Set Valued Functions written by Alexander Nelson Cornelius and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Funtions, Continuous categories.

Much is known about inverse limits of compact spaces with continuous bonding maps. When the requirement that the bonding maps be continuous functions is relaxed, to allow for upper semi-continuous set-valued functions, many of the standard tools used to study inverse limit spaces are no longer available. Also, the structure of the inverse limit becomes more complicated. In this dissertation, the structure of compact subsets of the inverse limit is studied. Necessary and sufficient conditions are given for a compact subset of an inverse limit to be the inverse limit of its projections. Weak crossovers are introduced and used to describe the relationship between a set and the inverse limit of its projections. In the process of examining weak crossovers, tools with potentially broader applications are developed. When set-valued bonding maps are continuous and can be written as a union of continuous functions, sufficient conditions to make the inverse limit a Hausdorff continuum are given. It is also shown that, with another assumption, the inverse limit is in fact decomposable. When the bonding map can be written as a union of set-valued functions between compact subsets of the factor space, a description of the inverse limit is given. This uses a generalization of the itinerary of a point.

Set Valued Force Laws

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Author : Christoph Glocker
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Set Valued Force Laws written by Christoph Glocker 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 2013-11-11 with Science categories.

As one of the oldest natural sciences, mechanics occupies a certain pioneering role in determining the development of exact sciences through its interaction with mathematics. As a matter of fact, there is hardly an area in mathematics that hasn't found an application of some form in mechanics. It is thus almost inevitable that theoretical methods in mechanics are highly developed and laid out on different levels of abstraction. With the spread of digital processors this goes as far as the implementation in commercial computer codes, where the user is merely con fronted on the surface with the processes that run in the background, i. e. mechan ics as such: in teaching and research, as well as in the context of industry, me chanics is much more, and must remain much more than the mere production of data with the help of a processor. Mechanics, as it is talked about here, tradition ally includes a wide spectrum, ranging from applied mechanics, analytical and technical mechanics to modeling. and experimental mechanics, as well as technical realization. It also includes the subdisciplines of rigid body mechanics, continuum mechanics, or fluid mechanics, to mention only a few. One of the fundamental and most important concepts used by nearly all natural sciences is the concept of linearization, which assumes the differentiability of mappings. As a matter of fact, all of classical mechanics is based on the avail ability of this quality.