Weakly <i>κ</i>-compact topological spaces

Abstract A weaker variant of κ -compactness is introduced and investigated, namely, weak κ -compactness, where κ is a regular uncountable cardinal. It is shown that these two notions coincide when κ is a strongly compact cardinal. The existence of a weakly κ -compact extension for a Tychonoff space is proved. Weak κ -compactness can also be defined by demanding that a certain equivalence holds between certain classes of Baire measures. Finally, κ -measure-compact spaces are introduced and studied.