Topological Algebras - 1st Edition - ISBN: 9780720407242, 9780080871356

Topological Algebras, Volume 24

1st Edition

Series Editors: Edward Beckenstein Lawrence Narici Charles Suffel
eBook ISBN: 9780080871356
Imprint: North Holland
Published Date: 1st January 1977
Page Count: 369
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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:
Imprint:
North Holland
eBook ISBN:
9780080871356

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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