Condensations with extra properties

Abstract

We show that there are locally compact spaces that can be condensed onto separable spaces but not onto compact separable spaces. We also show that for every cardinal $\kappa$ there is a locally compact topological group of cardinality $2^\kappa$ that can be condensed onto a compact space but not onto a compact topological group. These answer some questions of Arhangel'skii and Buzyakova.