On cellular-compactness and related properties

Abstract

We study three subclasses of the class of pseudocompact spaces. We answer two open questions concerning cellular-compact spaces and another concerning cellular-Lindelof spaces and introduce and study three other subclasses of the class of feebly compact spaces, namely the class of cellular-countably-compact spaces, that of the cellular-sequentially-compact spaces and that of the cellular-compact-metrizable spaces. We show that it is independent of ZFC whether or not a cellular-compact-metrizable LOTS is metrizable.