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eBook Categorical Structure of Closure Operators: With Applications to Topology, Algebra and Discrete Mathematics (Mathematics and Its Applications) download

by D. Dikranjan,Walter Tholen

eBook Categorical Structure of Closure Operators: With Applications to Topology, Algebra and Discrete Mathematics (Mathematics and Its Applications) download ISBN: 9048146313
Author: D. Dikranjan,Walter Tholen
Publisher: Springer; Softcover reprint of hardcover 1st ed. 1995 edition (December 3, 2010)
Language: English
Pages: 358
ePub: 1654 kb
Fb2: 1474 kb
Rating: 4.7
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Category: Math Sciences
Subcategory: Mathematics

Mathematics and Its Applications. Authors: Dikranjan, Dikran, Tholen, Walter. Bibliographic Information. Categorical Structure of Closure Operators.

Mathematics and Its Applications. With Applications to Topology, Algebra and Discrete Mathematics. Mathematics and Its Applications.

Categorical structure of closure operators with applications to topology, algebra, and discrete mathematics. Dikran N. Dikranjan, Walter Tholen. Download (djvu, 1. 2 Mb) Donate Read.

Closure Operators, Functors, Factorization Systems. 7. Subcategories Defined by Closure Operators. Dikran Dikranjan, Walter Tholen. 6. Regular Closure Operators. 8. Epimorphisms and Cowellpoweredness. 9. Dense Maps and Pullback Stability. Index of Definitions. 1. Preliminaries on Subobjects, Images, and Inverse Images. 2. Basic Properties of Closure Operators. 3. Examples of Closure Operators. 4. Operations on Closure Operators. 5. Closure Operators, Functors, Factorization Systems.

Mathematics and Its Applications

Mathematics and Its Applications. Kirja 346. D. Dikranjan Walter Tholen9. 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.

With Applications to Topology, Algebra and Discrete Mathematics. b ianment of Mathematics, &Wvenity of Udine, U Pw Italy. Application to topological groups . 0 Closure operators and CS-valued functors . 1 Closure-structured categories, uniform spaces . 2 Pointed modifications of closure operators . 3 Closure operators and adjoint functors . 4 External closure operators.

Mathematics and Its Applications D. Dikranjan and w. Tholen . Discrete Mathematics with Applications

Mathematics and Its Applications D. Tholen Categorical Structure of Closure Operators Kluwer Academic. Applications of Categorical Algebra. Discrete Mathematics with Applications. Discrete Mathematics with Applications Discrete Mathematics with Applications. Preface A journey of a thousand miles begins with a single step.

ISBN13: 9780792337720. More Books . ABOUT CHEGG.

D With Applications to Topology, Algebra and Discrete Mathematics.

Categorical Structure of Closure Operators D. Dikranjan; Walter Tholen Springer 9780792337720 : This study provides a comprehensive categorical theory of closure operators, with applications . 1995 Серия: Mathematics and Its Applications Язык: ENG Размер: 2. 9 x 1. 0 x . 4 cm Основная тема: Mathematics Подзаголовок: With Applications to Topology, Algebra and Discrete Mathematics Рейтинг

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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.