The hyperspace of a semi-Eberlein compact space is semi-Eberlein

Abstract

We prove, using r-skeletons, that if X is a semi-Eberlein compact space, then its hyperspace of compact subsets is a semi-Eberlein compact space. We prove that c-skeletons can be induced on the hyperspaces of compact subsets of a space admitting a c-skeleton, and we characterize the presence of full c-skeletons on function spaces Cp(X). Finally, we characterize ω-monotone assignments of pseudobases on subspaces of ω1. These results answer some open questions published in [11], [2] and [16].