Radical Classes of Lattice-Ordered Groups vs. Classes of Compact Spaces |
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Authors: | Darnel Michael R Martinez Jorge |
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Institution: | (1) Department of Mathematics, Indiana University South Bend, South Bend, IN, 46634, U.S.A;(2) Department of Mathematics, University of Florida, Gainesville, FL, 32611-8105, U.S.A |
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Abstract: | 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 gG
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 -group G is in Y(F) if and only if, for each pair of disjoint countably generated polars P and Q, G=P
+Q
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Keywords: | F-spaces -disconnected spaces" target="_blank">gif" alt="kappa" align="BASELINE" BORDER="0">-disconnected spaces completeness of a class laterally separated radical class of -groups" target="_blank">gif" alt="ell" align="BASELINE" BORDER="0">-groups spectral space stranded primes Yosida space |
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