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| Paper IPM / M / 11184 |
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| Abstract: | |
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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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