Comfort, W. W. On the ”fragmentation” of certain pseudocompact groups. (English) Zbl 0592.22006 Bull. Greek Math. Soc. 25, 1-13 (1984). Summary: We show for \(\omega^+\leq \alpha \leq {\mathfrak c}\) and S a closed subgroup of the circle group \({\mathbb{T}}\) that for every dense, pseudocompact subgroup G of \(S^{\alpha}\) there is a family \(\{G_{\eta}:\) \(\eta <{\mathfrak c}\}\) of dense, pseudocompact subgroups of G which are nearly disjoint in the sense that \(G_{\eta}\cap G_{\eta '}=\{e\}\) for \(\eta <\eta '<{\mathfrak c}\). It follows that for every compact, abelian group K of uncountable weight there is a \({\mathfrak c}\)-sequence \(\{K_{\eta}:\) \(\eta <{\mathfrak c}\}\) of dense, pseudocompact subgroups of K such that \(K_ n\supsetneqq K_{\eta +1}\) for \(\eta <{\mathfrak c}\); one may arrange that \(\cap_{\eta}K_{\eta}\) is dense in K and pseudocompact. Cited in 5 Documents MSC: 22C05 Compact groups 54D30 Compactness Keywords:pseudocompact; compact, abelian group; uncountable weight; \({\mathfrak c}\)- sequence; dense PDFBibTeX XMLCite \textit{W. W. Comfort}, Bull. Greek Math. Soc. 25, 1--13 (1984; Zbl 0592.22006) Full Text: EuDML