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  • 1 Semnan University Department of Mathematics P.O. Box 35195-363 Semnan Iran
  • 2 Institute for Research in Fundamental Sciences (IPM) School of Mathematics and Computer Science, Amirkabir University of Technology and School of Mathematics P.O. Box 19395-5746 Tehran Iran
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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 Hausdorff 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 finite subsets forms a base for it. Finally, we prove that K0(X), Hd) is Smyth-complete if (X, d) is Smyth-complete and all compact subsets of X are d−1-precompact.