Topological Guide and Related Structures - Couverture rigide

Arhangel'skii, Alexander; Tkachenko, Mikhail

 
9789078677062: Topological Guide and Related Structures
Couverture rigide
ISBN 10 : 9078677066 ISBN 13 : 9789078677062
Editeur : Atlantis Press, 2008

Synopsis

This book presents a large amount of material, both classic and recent (on occasion, unpublished) about the relations of Algebra and Topology. It therefore belongs to the area called Topological Algebra. More specifically, the objects of the study are subtle and sometimes unexpected phenomena that occur when the continuity meets and properly feeds an algebraic operation. Such a combination gives rise to many classic structures, including topological groups and semigroups, paratopological groups, etc. Special emphasis is given to tracing the influence of compactness and its generalizations on the properties of an algebraic operation, causing on occasion the automatic continuity of the operation. The main scope of the book, however, is outside of the locally compact structures, thus distinguishing the monograph from a series of more traditional textbooks.

The book is unique in that it presents very important material, dispersed in hundreds of research articles, not covered by any monograph in existence. The reader is gently introduced to an amazing world at the interface of Algebra, Topology, and Set Theory. He/she will find that the way to the frontier of the knowledge is quite short — almost every section of the book contains several intriguing open problems whose solutions can contribute significantly to the area.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

This book presents a large amount of material, both classic and recent (on occasion, unpublished) about the relations of Algebra and Topology. It therefore belongs to the area called Topological Algebra. More specifically, the objects of the study are subtle and sometimes unexpected phenomena that occur when the continuity meets and properly feeds an algebraic operation. Such a combination gives rise to many classic structures, including topological groups and semigroups, paratopological groups, etc. Special emphasis is given to tracing the influence of compactness and its generalizations on the properties of an algebraic operation, causing on occasion the automatic continuity of the operation. The main scope of the book, however, is outside of the locally compact structures, thus distinguishing the monograph from a series of more traditional textbooks.

The book is unique in that it presents very important material, dispersed in hundreds of research articles, not covered by any monograph in existence. The reader is gently introduced to an amazing world at the interface of Algebra, Topology, and Set Theory. He/she will find that the way to the frontier of the knowledge is quite short — almost every section of the book contains several intriguing open problems whose solutions can contribute significantly to the area.

Revue de presse

Topological Groups and Related Structures provides an extensive overview of techniques and results in the topological theory of topological groups. This overview goes sufficiently deep and is detailed enough to become a useful tool for both researchers and students. --Mathematical Reviews

Thus, it provides a systematic and comprehensive exposition of most main results accomplished in the are area since the last half of the twentieth century. Basically all results presented by the authors are given with complete and detailed proofs. Moreover, they are accompanied with many pertinent examples and related open questions for future research. A very attractive section on historical comments and references is given at the end of every chapter. It is highly recommended to all people interested in the topological structure of topological groups. --Zentralblatt MATH

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Atlantis Press
Date d'édition
2008
Langue
anglais
ISBN 10 
9078677066
ISBN 13 
9789078677062
Reliure
Relié
Nombre de pages
800
Coordonnées du fabricant
non disponible
Personne responsable
gpsr@libri.de
gpsr@libri.de

Friedensallee 273
Hamburg
22763
Allemagne