Show simple item record Stokke, Ross Thomas en_US 2007-05-15T15:20:52Z 2007-05-15T15:20:52Z 1997-05-01T00:00:00Z en_US
dc.description.abstract Given a topological space X, the ring C(X) of continuous real-valued functions on X is endowed with what is called the 'uniform metric'. The closed ideals of C(X) in this metric are of much interest, and a new, purely algebraic characterization of these ideals is provided. The result is applied to describe the real maximal ideals of C(X), and to characterize several types of topological spaces. A $\Phi$-algebra is an archimedian lattice-ordered algebra closely related to C(X). z-ideals in $\Phi$-algebras are examined, and as an application to this study, several conditions equivalent to regularity in a $\Phi$-algebra are obtained. A uniform metric may also be placed upon a $\Phi$-algebra, and in this metric the closed ideals of a $\Phi$-algebra have received a fair amount of research attention. We give necessary and sufficient conditions to ensure that an ideal of a $\Phi$-algebra is closed, and for two broad classes of $\Phi$-algebras show that these conditions are equivalent, thus generalizing our characterization from the C(X) case. en_US
dc.format.extent 3526121 bytes
dc.format.extent 184 bytes
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dc.language en en_US
dc.language.iso en_US
dc.title Closed ideals in C(X) and related algebraic structures en_US Mathematics en_US Master of Science (M.Sc.) en_US

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