Radical Classes of Lattice-Ordered Groups vs. Classes of Compact Spaces
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- 作者：Michael R. Darnel and Jorge Martinez
- 关键词：F ; spaces ; ; disconnected spaces ; completeness of a class ; laterally separated ; radical class of ; groups ; spectral space ; stranded primes ; Yosida space
- 刊名：Order
- 出版时间：2002
- 出版年：2002
- 期刊代码：55_01678094
- 类别：ch
- 卷：19
- 期：1
- 页码：35-72
- 数据来源：sp
摘要
For a given class T of compact Hausdorff spaces, let Y(T) denote the class of -groups G such that for each gG, the Yosida space Y(g) of g belongs to T. Conversely, if R is a class of ;-groups, then T(R) stands for the class of all spaces which are homeomorphic to a Y(g) for some gGR. The correspondences TY(T) and RT(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 gGY(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 -group G is in Y(F) if and only if, for each pair of disjoint countably generated polars P and Q, G=P+Q.