Topological Algebras

Edward Beckenstein, Lawrence Narici, Charles Suffel

• Publisher: North Holland
• Year: 2011
• ISBN:
  9780080871356
• Topic: Mathematics
• Subtopic: Algebraic Geometry
• Index: Mathematics

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–Cech compactification and the Wallman compactification play an important role in characterizing the maximal ideals of certain topological algebras.

Table of contents

• Front Cover
• Topological Algebras
• Copyright Page
• Contents
• Chapter 0. Fundamentals
• Chapter 1. Algebras of Continuous Functions
• Chapter 2. Topological Vector Spaces of Continuous Functions
• Chapter 3. Lattices and Wallman Compactifications
• Chapter 4. Topological Algebras
• Chapter 5. Hull-Kernel Topologies
• Chapter 6. LB-Algebras
• References
• Index of Symbols
• Index