Abstract
A P-set is a closed set which is interior to any zero set (closed G δ {G_\delta } ) which contains it. Henriksen and Isbell showed that the ’support set’ in β N ∖ N \beta N\backslash N of a nonnegative regular matrix is a P-set. We show that each such support set contains a family of 2 c {2^c} pairwise disjoint perfect nowhere dense P-sets, so that not every P-set comes from a matrix. Moreover, each of the P-sets produced is the support of a Borel probability measure on β N ∖ N \beta N\backslash N .
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