Compactifications of a Pixley–Roy hyperspace

For a Hausdorff space X  , let PR(X)PR(X) be the Pixley–Roy hyperspace of X. Dow and Moore [10, Proposition 2.13] noted that no compactification of PR(2ω)PR(2ω) has countable tightness. In this paper, we will discuss when PR(X)PR(X) has a compactification of countable tightness in general. Among other things, we will show that if a Pixley–Roy hyperspace has a compactification of countable tightness, then it will actually have a Corson compactification.