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On \(\omega^*\) and absolutely divergent series. (English) Zbl 0840.03033

Summary: We summarize some of our former results on series, ultrafilters and cardinal characteristics in a new unified manner by Galois-Tukey connections. Using some new observations about the connection between separative factorization of the comparison ordering of divergent series and \(\omega^*\) we get a new insight into these older results. This gives a new type of characterization of points of \(\omega^*\) and a (possibly) new sort of duality.

MSC:

03E05 Other combinatorial set theory
54D40 Remainders in general topology
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
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