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  • Author or Editor: M. Pourmahdian x
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We study the hyperspace K 0(X) of non-empty compact subsets of a Smyth-complete quasi-metric space (X, d). We show that K 0(X), equipped with the Hausdorff quasi-pseudometric H d forms a (sequentially) Yoneda-complete space. Moreover, if d is a T 1 quasi-metric, then the hyperspace is algebraic, and the set of all finite subsets forms a base for it. Finally, we prove that K 0(X), H d) is Smyth-complete if (X, d) is Smyth-complete and all compact subsets of X are d −1-precompact.

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