Topological Groups & Related Structures: An Introduction to Topological Algebra - Hardcover

Alexander Arhangel'skii And Mikhail Tkachenko

Hardcover

ISBN 10: 9078677066 ISBN 13: 9789078677062

Publisher: World Scientific Publishing Company, 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This book presents a large amount of material, both classic and recent (on occasion, unpublished) about the relations of Algebra and Topology.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.

About this title

Review

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

Edition details

• Publisher: World Scientific Publishing Company
• Publication date: 2008
• Language: English
• ISBN 10: 9078677066
• ISBN 13: 9789078677062
• Binding: Hardcover
• Number of pages: 800