Following the first four chapters, which comprise the body of an introductory course on compact groups, the volume addresses the general theory of (linear) Lie groups; the structure of compact Lie groups; duality for abelian topological groups; compact abelian groups; the structure of compact groups and their actions; the structure of free compact groups; and cardinal invariants of compact groups. The initial chapters are for the beginning graduate student who has had basic analysis, algebra, elementary functional analysis up through the elements of Banach spaces and Banach algebras, and possesses a background in point set topology. Later chapters require more background knowledge, including some algebraic topology. The volume is useful for students and also for mathematicians in various specialties who want material on compact groups that is otherwise difficult to access. Annotation copyrighted by Book News, Inc., Portland, ORA Primer for the Student, a Handbook for the Expert Karl Heinrich Hofmann, Sidney A. Morris ... there is a u 6 U and gu, v 6 Gu such that gu, v an V~lg. Now gu, vu = u. Thus g-u e Vgu, v-u = V.u C V-U. Hence g-U C V-U and since U and V were 10.
|Title||:||The Structure of Compact Groups|
|Author||:||Karl Heinrich Hofmann, Sidney A. Morris|
|Publisher||:||Walter de Gruyter - 1998-01-01|