Topological Algebras, Volume 24
1st Edition
Description
This book discusses general topological algebras; space C(T,F) of continuous functions mapping T into F as an algebra only (with pointwise operations); and C(T,F) endowed with compact-open topology as a topological algebra C(T,F,c). It characterizes the maximal ideals and homomorphisms closed maximal ideals and continuous homomorphisms of topological algebras in general and C(T,F,c) in particular. A considerable inroad is made into the properties of C(T,F,c) as a topological vector space. Many of the results about C(T,F,c) serve to illustrate and motivate results about general topological algebras. Attention is restricted to the algebra C(T,R) of real-valued continuous functions and to the pursuit of the maximal ideals and real-valued homomorphisms of such algebras. The chapter presents the correlation of algebraic properties of C(T,F) with purely topological properties of T. The Stone–Čech compactification and the Wallman compactification play an important role in characterizing the maximal ideals of certain topological algebras.
Details
- No. of pages:
- 369
- Language:
- English
- Copyright:
- © North Holland 1977
- Published:
- 1st January 1977
- Imprint:
- North Holland
- eBook ISBN:
- 9780080871356
Ratings and Reviews
About the Series Editors
Edward Beckenstein Series Editor
Affiliations and Expertise
St. John's University, Notre Dame College, Staten island, New York
Lawrence Narici Series Editor
Affiliations and Expertise
St. John's University, Jamaica, New York
Charles Suffel Series Editor
Affiliations and Expertise
Stevens Institute of Technology, Hoboken, New Jersey