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Beschreibung
Presents the general theory of categorical closure operators together
with examples and applications to the most common categories, e.g.,
topological spaces, fuzzy topological spaces, groups, and abelian
groups. Part I deals with the general theory, starting with basic
definitions and gradually moving to more advanced properties. Part II
includes applications to the classical concepts of epimorphisms,
separation, compactness and connectedness. Every chapter ends with
exercises. A comprehensive bibliography and good index complete this
self-contained text, which appeals to graduate students and
researchers.
Presents the general theory of categorical closure operators together
with examples and applications to the most common categories, e.g.,
topological spaces, fuzzy topological spaces, groups, and abelian
groups. Part I deals with the general theory, starting with basic
definitions and gradually moving to more advanced properties. Part II
includes applications to the classical concepts of epimorphisms,
separation, compactness and connectedness. Every chapter ends with
exercises. A comprehensive bibliography and good index complete this
self-contained text, which appeals to graduate students and
researchers.
Zusammenfassung
Presents the general theory of categorical closure operators together
with examples and applications to the most common categories, e.g.,
topological spaces, fuzzy topological spaces, groups, and abelian
groups. Part I deals with the general theory, starting with basic
definitions and gradually moving to more advanced properties. Part II
includes applications to the classical concepts of epimorphisms,
separation, compactness and connectedness. Every chapter ends with
exercises. A comprehensive bibliography and good index complete this
self-contained text, which appeals to graduate students and
researchers.
Inhaltsverzeichnis
I GENERAL THEORY.- 1 Galois Connections.- 2 Some Categorical Concepts.- 3 Factorization Structures For Sinks.- 4 Closure Operators: Definition and Examples.- 5 Idempotency, Weak Heredity and Factorization Structures.- 6 Additivity, Heredity, Suprema and Infima of Closure Operators.- 7 Additional Descriptions of ? and ? and Subobject Orthogonality.- 8 A Diagram of Galois Connections of Closure Operators.- 9 Regular Closure Operators.- 10 Hereditary Regular Closure Operators.- 11 APPLICATIONS.- 11 Epimorphisms.- 12 Separation.- 13 Compactness.- 14 Connectedness.- 15 Connectedness in Categories with a Terminal Object.- 16 A Link between two Connectedness Notions.- 17 Different Constructions Related.- References.- List of Symbols.
Details
Erscheinungsjahr: 2012
Fachbereich: Arithmetik & Algebra
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xii
300 S.
ISBN-13: 9781461265047
ISBN-10: 1461265045
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Castellini, Gabriele
Hersteller: Birkhäuser
Birkhäuser Boston
Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße: 235 x 155 x 18 mm
Von/Mit: Gabriele Castellini
Erscheinungsdatum: 06.10.2012
Gewicht: 0,482 kg
Artikel-ID: 106118854