Topological Algebras
Elsevier (Publisher)
Published on 10. October 2011
369 pages
978-0-08-087135-6 (ISBN)
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-Cech compactification and the Wallman compactification play an important role in characterizing the maximal ideals of certain topological algebras.
More details
Other editions
Additional editions
Edward Beckenstein | etc.
Topological Algebras
Book
05/1977
North-Holland
€69.02
Article exhausted; check different version
Persons
Content
- Front Cover
- Topological Algebras
- Copyright Page
- Contents
- Chapter 0. Fundamentals
- 0.1 Topologies defined by families of functions
- 0.2 Uniformities defined by families of functions
- Chapter 1. Algebras of Continuous Functions
- 1.1 The Stone-Cech compactification
- 1.2 Zero sets
- 1.3 Maximal ideals and z-filters
- 1.4 Maximal ideals and the Stone-Cech compactification
- 1.5 Replete spaces
- 1.6 Characters and uT
- 1.7 0-1 measures, ßT, and Ulam cardinals
- 1.8 Shirota's theorem on repleteness
- Chapter 2. Topological Vector Spaces of Continuous Functions
- 2.1 Metrizability of C(T,F,c) and hemicompactness
- 2.2 Completeness and kR -spaces
- 2.3 k-spaces, kR -spaceg and pseudof inite spaces
- 2.4 Continuous 8ual of C(T,F,c) and support
- 2.5 Barreledness of C(T,F,c)
- 2.6 Bornologicity of C(T,F,c)
- 2.7 Separability of C(T,F,c)
- 2.8 The bornology of C(T,F,c)
- Chapter 3. Lattices and Wallman Compactifications
- 3.1 Lattices
- 3.2 Lattices and associated compactifications
- 3.3 Wallman compactifications of topological spaces
- 3.4 ßT and Wallman compactifications
- 3.5 A class of Wallman-type compactifications
- 3.6 Equivalent Wallman spaces
- Chapter 4. Topological Algebras
- 4.1 Topological algebras
- 4.2 Multiplicative sets and multiplicative seminorms
- 4.3 Locally m-convex algebras
- 4.4 Final topologies and quotients
- 4.5 The factor algebras
- 4.6 Complete LMCH algebras and projective limits
- 4.7 The spectrum
- 4.8 Q-algebras and algebras with continuous inverse
- 4.9 Topological division algebras and the Gelfand-Mazur theorem
- 4.10 Maximal ideals and homomorphisms
- 4.11 The radical and derivations
- 4.12 Some elements of Gelfand theory
- 4.13 Continuity of homomorphisms
- Chapter 5. Hull-Kernel Topologies
- 5.1 Hull-kernel topologies
- 5.2 Regular algebras and normality conditions
- 5.3 Condition hH
- 5.4 M as a Wallman compactification of Mc
- 5.5 The X-repletion of Mc
- 5.6 Frechet algebras
- Chapter 6. LB-Algebras
- 6.1 LB-algebras
- 6.2 Some properties of LB-algebras
- 6.3 Complete LMC LB-algebras
- References
- Index of Symbols
- Index
