A short note on hit-and-miss hyperspaces

René Bartsch, Harry Poppe


Based on some set-theoretical observations, compactness results are given for general hit-and-miss hyperspaces. Compactness here is sometimes viewed splitting into “κ-Lindelöfness” and “κ-compactness” for cardinals κ. To focus only hit-and-miss structures, could look quite old-fashioned, but some importance, at least for the techniques, is given by a recent result, [8], of Som Naimpally, to who this article is hearty dedicated.


Hit-and-miss topology; Compactness; Relative completeness; Relative compact unions; Upper Vietoris topology

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