Name
Abstract | ||
|---|---|---|
For a given class T of compact Hausdor spaces, let Y(T ) denote the class of '-groups G such that for each g2 G, the Yosida space Y (g) of g belongs toT . Conversely, ifR is a class of '-groups, then T(R) stands for the class of all spaces which are homeomorphic to a Y (g) for some g2 G2 R. The correspondencesT 7!Y(T ) andR7!T(R) are examined with regard to several closure properties of classes. Several sections are devoted to radical classes of '- groups whose Yosida spaces are zero-dimensional. There is a thorough discussion of hyper-projectable '-groups, followed by presentations on Y(e:d:), where e:d: denotes the class of compact extremally disconnected spaces, and, for each regular uncountable cardinal , the class Y(disc ), where disc stands for the class of all compact -disconnected spaces. Sample results follow. Every strongly projectable '-group lies in Y(e:d:). The '-group G lies in Y(e:d:) if and only if for each g2 G Y (g) is zero-dimensional and the boolean algebra of components of g, comp(g), is complete. Corresponding results hold for Y(disc ). Finally, there is a discussion of Y(F ), with F standing for the class of compact F -spaces. It is shown that an archimedean'-groupG is inY(F ) if and only if, for each pair of disjoint countably generated polars P and Q, G = P? +Q?. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1023/A:1015259615457 | Order |
Keywords | Field | DocType |
F,-spaces,κ-disconnected spaces,completeness of a class,laterally separated,radical class of ℓ-groups,spectral space,stranded primes,Yosida space | Discrete mathematics,Combinatorics,Uncountable set,Disjoint sets,Lattice (order),Spectral space,If and only if,Hausdorff space,Boolean algebra,Mathematics,Homeomorphism | Journal |
Volume | Issue | ISSN |
19 | 1 | 1572-9273 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael R. Darnel | 1 | 0 | 0.68 |
| Jorge Martínez | 2 | 95 | 17.02 |