Generalizations of quasi-k spaces

Abstract

Four classes of spaces are considered, all generalizing quasi-k spaces.The implications among these classes under the assumptions that the spaces are Hausdorff, regular, and normal are briefly discussed. A regular relatively bi-quasi-k space which is not quasi-k is constructed, answering a question of Olson. The continuum hypothesis is used to construct a relatively quasi-k space that is not quasi-k.