Abstract
A space X is said to be selectively separable (=M-separable) if for every sequence {Dn:n∈ω} of dense subsets of X, there are finite sets Fn⊂Dn (n∈ω) such that ⋃{Fn:n∈ω} is dense in X. We show that the Pixley–Roy hyperspace PR(X) of a space X is selectively separable if and only if X is countable and every finite power of X has countable fan-tightness for finite sets. As an application, under b=d there are selectively separable Pixley–Roy hyperspaces PR(X), PR(Y) such that PR(X)×PR(Y) is not selectively separable.
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