T0*-compactification in the hyperspace

A *-compactification of a T 0 quasi-uniform space ( X , U ) is a compact T 0 quasi-uniform space ( Y , V ) that has a T ( V ∨ V − 1 ) -dense subspace quasi-isomorphic to ( X , U ) . In this paper we study when the hyperspace with the Hausdorff–Bourbaki quasi-uniformity is *-compactifiable and describe some of its *-compactifications.