Closed ideals in C(X) and related algebraic structures
| dc.contributor.author | Stokke, Ross Thomas | en_US |
| dc.date.accessioned | 2007-05-15T15:20:52Z | |
| dc.date.available | 2007-05-15T15:20:52Z | |
| dc.date.issued | 1997-05-01T00:00:00Z | en_US |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Master of Science (M.Sc.) | 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 | |
| dc.format.mimetype | application/pdf | |
| dc.format.mimetype | text/plain | |
| dc.identifier.uri | http://hdl.handle.net/1993/905 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.title | Closed ideals in C(X) and related algebraic structures | en_US |
| dc.type | master thesis | en_US |