Condensations with extra properties

Abstract We show that there are locally compact spaces that can be condensed on separable spaces, but not on 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 on a compact space but not on a compact topological group. These answer some questions of Arhangel’skii and Buzyakova.