Completeness of hyperspaces of compact subsets of quasi-metric spaces |
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| Authors: | M. Ali-Akbari M. Pourmahdian |
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| Affiliation: | 1.Department of Mathematics,Semnan University,Semnan,Iran;2.School of Mathematics and Computer Science, Amirkabir University of Technology and School of Mathematics,Institute for Research in Fundamental Sciences (IPM),Tehran,Iran |
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| Abstract: | 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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