René Bartsch, Harry Poppe
A short note on hit-and-miss hyperspaces
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

54B20 Hyperspaces

54D30 Compactness

Abstract: Based on some set-theoretical observations, compactness results
are given for general hit-and-miss hyperspaces. Compactness here is
sometimes viewed splitting into "$\kappa$-Lindel\"ofness" and "$\kappa$-compactness"
for cardinals $\kappa$. 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 of Som Naimpally, to who this article is hearty dedicated.
Keywords: hit-and-miss topology, compactness,relative completeness, relative compact unions, upper Vietoris topology