Introduction to Topological Groups

Nonfiction, Science & Nature, Mathematics, Topology
Cover of the book Introduction to Topological Groups by Dr. Taqdir Husain, Dover Publications
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Author: Dr. Taqdir Husain ISBN: 9780486828206
Publisher: Dover Publications Publication: January 10, 2018
Imprint: Dover Publications Language: English
Author: Dr. Taqdir Husain
ISBN: 9780486828206
Publisher: Dover Publications
Publication: January 10, 2018
Imprint: Dover Publications
Language: English

Suitable for advanced undergraduates and graduate students in mathematics, this introduction to topological groups presumes familiarity with the elementary concepts of set theory, elements of functional analysis, functions of real and complex variables, and the theory of functions of several variables. Chapters I to V deal with the algebraico-topological aspect of the subject, and Chapters VI to IX emphasize its analytical aspect.
After an introductory chapter on the fundamentals of topology and group theory, the treatment explores semitopological groups and the general theory of topological groups. An elementary study of locally compact topological groups is followed by proofs of the open homomorphism and closed graph theorems in a very general setting. Succeeding chapters examine the rudiments of analysis on topological groups. Topics include the Harr measure, finite-dimensional representations of groups, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras.

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Suitable for advanced undergraduates and graduate students in mathematics, this introduction to topological groups presumes familiarity with the elementary concepts of set theory, elements of functional analysis, functions of real and complex variables, and the theory of functions of several variables. Chapters I to V deal with the algebraico-topological aspect of the subject, and Chapters VI to IX emphasize its analytical aspect.
After an introductory chapter on the fundamentals of topology and group theory, the treatment explores semitopological groups and the general theory of topological groups. An elementary study of locally compact topological groups is followed by proofs of the open homomorphism and closed graph theorems in a very general setting. Succeeding chapters examine the rudiments of analysis on topological groups. Topics include the Harr measure, finite-dimensional representations of groups, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras.

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