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Paper   IPM / M / 11184
School of Mathematics
  Title:   Completeness of hyperspaces of compact subsets of quasi-metric spaces
  Author(s):  M. Pourmahdian (Joint with M. Aliakbari)
  Status:   Published
  Journal: Acta Math. Hungar.
  Vol.:  127
  Year:  2010
  Pages:   260-272
  Supported by:  IPM
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 that 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.

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