Abstract

We study the hyperspace K0(X) of non-empty compact subsets of a Smyth-complete quasi-metric space (X;d). We show that K0(X), equipped with the Hausdorfi quasi-pseudometric Hd forms a (sequentially) Yoneda-complete space. Moreover, if d is a T1 quasi-metric, then the hyperspace is algebraic, and the set of all flnite subsets forms a base for it. Finally, we prove that i K0(X);Hd ¢ is Smyth-complete if (X;d) is Smyth-complete and all compact subsets of X are d i1 -precompact.

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