Categorical Structure Of Closure Operators
Download Categorical Structure Of Closure Operators full books in PDF, epub, and Kindle. Read online free Categorical Structure Of Closure Operators ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author | : D. Dikranjan |
Publisher | : Springer Science & Business Media |
Total Pages | : 373 |
Release | : 2013-04-09 |
Genre | : Mathematics |
ISBN | : 9401584001 |
Download Categorical Structure of Closure Operators Book in PDF, Epub and Kindle
Our motivation for gathering the material for this book over aperiod of seven years has been to unify and simplify ideas wh ich appeared in a sizable number of re search articles during the past two decades. More specifically, it has been our aim to provide the categorical foundations for extensive work that was published on the epimorphism- and cowellpoweredness problem, predominantly for categories of topological spaces. In doing so we found the categorical not ion of closure operators interesting enough to be studied for its own sake, as it unifies and describes other significant mathematical notions and since it leads to a never-ending stream of ex amples and applications in all areas of mathematics. These are somewhat arbitrarily restricted to topology, algebra and (a small part of) discrete mathematics in this book, although other areas, such as functional analysis, would provide an equally rich and interesting supply of examples. We also had to restrict the themes in our theoretical exposition. In spite of the fact that closure operators generalize the uni versal closure operations of abelian category theory and of topos- and sheaf theory, we chose to mention these aspects only en passant, in favour of the presentation of new results more closely related to our original intentions. We also needed to refrain from studying topological concepts, such as compactness, in the setting of an arbitrary closure-equipped category, although this topic appears prominently in the published literature involving closure operators.
Author | : Gabriele Castellini |
Publisher | : Springer Science & Business Media |
Total Pages | : 300 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 0817682341 |
Download Categorical Closure Operators Book in PDF, Epub and Kindle
This book presents the general theory of categorical closure operators to gether with a number of examples, mostly drawn from topology and alge bra, which illustrate the general concepts in several concrete situations. It is aimed mainly at researchers and graduate students in the area of cate gorical topology, and to those interested in categorical methods applied to the most common concrete categories. Categorical Closure Operators is self-contained and can be considered as a graduate level textbook for topics courses in algebra, topology or category theory. The reader is expected to have some basic knowledge of algebra, topology and category theory, however, all categorical concepts that are recurrent are included in Chapter 2. Moreover, Chapter 1 contains all the needed results about Galois connections, and Chapter 3 presents the the ory of factorization structures for sinks. These factorizations not only are essential for the theory developed in this book, but details about them can not be found anywhere else, since all the results about these factorizations are usually treated as the duals of the theory of factorization structures for sources. Here, those hard-to-find details are provided. Throughout the book I have kept the number of assumptions to a min imum, even though this implies that different chapters may use different hypotheses. Normally, the hypotheses in use are specified at the beginning of each chapter and they also apply to the exercise set of that chapter.
Author | : Dikran Dikranjan |
Publisher | : Springer |
Total Pages | : 358 |
Release | : 2013-01-08 |
Genre | : Mathematics |
ISBN | : 9789401584012 |
Download Categorical Structure of Closure Operators Book in PDF, Epub and Kindle
Our motivation for gathering the material for this book over aperiod of seven years has been to unify and simplify ideas wh ich appeared in a sizable number of re search articles during the past two decades. More specifically, it has been our aim to provide the categorical foundations for extensive work that was published on the epimorphism- and cowellpoweredness problem, predominantly for categories of topological spaces. In doing so we found the categorical not ion of closure operators interesting enough to be studied for its own sake, as it unifies and describes other significant mathematical notions and since it leads to a never-ending stream of ex amples and applications in all areas of mathematics. These are somewhat arbitrarily restricted to topology, algebra and (a small part of) discrete mathematics in this book, although other areas, such as functional analysis, would provide an equally rich and interesting supply of examples. We also had to restrict the themes in our theoretical exposition. In spite of the fact that closure operators generalize the uni versal closure operations of abelian category theory and of topos- and sheaf theory, we chose to mention these aspects only en passant, in favour of the presentation of new results more closely related to our original intentions. We also needed to refrain from studying topological concepts, such as compactness, in the setting of an arbitrary closure-equipped category, although this topic appears prominently in the published literature involving closure operators.
Author | : Werner Ghler |
Publisher | : World Scientific |
Total Pages | : 378 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9789812702418 |
Download Categorical Structures and Their Applications Book in PDF, Epub and Kindle
The book collects original research papers on applied categorical structures, most of which have been presented at the North-West European Category Seminar 2003 in Berlin. The spectrum of these mathematical results reflects the varied interests of Horst Herrlich OCo one of the leading category theorists of the world OCo to whom this volume is dedicated in view of his 65th birthday. The book contains applications of categorical methods in various branches of mathematics such as algebra, analysis, logic and topology, as well as fuzzy structures and computer science. At the end of the book the reader will find a complete list of Horst HerrlichOCOs publications. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences."
Author | : Jesse Elliott |
Publisher | : Springer Nature |
Total Pages | : 490 |
Release | : 2019-11-30 |
Genre | : Mathematics |
ISBN | : 3030244016 |
Download Rings, Modules, and Closure Operations Book in PDF, Epub and Kindle
This book presents a systematic exposition of the various applications of closure operations in commutative and noncommutative algebra. In addition to further advancing multiplicative ideal theory, the book opens doors to the various uses of closure operations in the study of rings and modules, with emphasis on commutative rings and ideals. Several examples, counterexamples, and exercises further enrich the discussion and lend additional flexibility to the way in which the book is used, i.e., monograph or textbook for advanced topics courses.
Author | : Jürgen Koslowski |
Publisher | : Springer Science & Business Media |
Total Pages | : 285 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461213703 |
Download Categorical Perspectives Book in PDF, Epub and Kindle
"Categorical Perspectives" consists of introductory surveys as well as articles containing original research and complete proofs devoted mainly to the theoretical and foundational developments of category theory and its applications to other fields. A number of articles in the areas of topology, algebra and computer science reflect the varied interests of George Strecker to whom this work is dedicated. Notable also are an exposition of the contributions and importance of George Strecker's research and a survey chapter on general category theory. This work is an excellent reference text for researchers and graduate students in category theory and related areas. Contributors: H.L. Bentley * G. Castellini * R. El Bashir * H. Herrlich * M. Husek * L. Janos * J. Koslowski * V.A. Lemin * A. Melton * G. Preuá * Y.T. Rhineghost * B.S.W. Schroeder * L. Schr"der * G.E. Strecker * A. Zmrzlina
Author | : Habil Werner Gahler |
Publisher | : World Scientific |
Total Pages | : 356 |
Release | : 2004-09-28 |
Genre | : Mathematics |
ISBN | : 981448170X |
Download Categorical Structures And Their Applications - Proceedings Of The North-west European Category Seminar Book in PDF, Epub and Kindle
The book collects original research papers on applied categorical structures, most of which have been presented at the North-West European Category Seminar 2003 in Berlin. The spectrum of these mathematical results reflects the varied interests of Horst Herrlich — one of the leading category theorists of the world — to whom this volume is dedicated in view of his 65th birthday. The book contains applications of categorical methods in various branches of mathematics such as algebra, analysis, logic and topology, as well as fuzzy structures and computer science. At the end of the book the reader will find a complete list of Horst Herrlich's publications.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Author | : Sh. Ayupov |
Publisher | : Springer Science & Business Media |
Total Pages | : 239 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 9401586055 |
Download Jordan, Real and Lie Structures in Operator Algebras Book in PDF, Epub and Kindle
The theory of operator algebras acting on a Hilbert space was initiated in thirties by papers of Murray and von Neumann. In these papers they have studied the structure of algebras which later were called von Neu mann algebras or W* -algebras. They are weakly closed complex *-algebras of operators on a Hilbert space. At present the theory of von Neumann algebras is a deeply developed theory with various applications. In the framework of von Neumann algebras theory the study of fac tors (i.e. W* -algebras with trivial centres) is very important, since they are comparatively simple and investigation of general W* -algebras can be reduced to the case of factors. Therefore the theory of factors is one of the main tools in the structure theory of von Neumann algebras. In the middle of sixtieth Topping [To 1] and Stormer [S 2] have ini tiated the study of Jordan (non associative and real) analogues of von Neumann algebras - so called JW-algebras, i.e. real linear spaces of self adjoint opera.tors on a complex Hilbert space, which contain the identity operator 1. closed with respect to the Jordan (i.e. symmetrised) product INTRODUCTION 2 x 0 y = ~(Xy + yx) and closed in the weak operator topology. The structure of these algebras has happened to be close to the struc ture of von Neumann algebras and it was possible to apply ideas and meth ods similar to von Neumann algebras theory in the study of JW-algebras.
Author | : Eraldo Giuli |
Publisher | : Springer Science & Business Media |
Total Pages | : 281 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9400902638 |
Download Categorical Topology Book in PDF, Epub and Kindle
Proceedings of the L'Aquila Conference 1994
Author | : Maria Cristina Pedicchio |
Publisher | : Cambridge University Press |
Total Pages | : 452 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9780521834148 |
Download Categorical Foundations Book in PDF, Epub and Kindle
Publisher Description