We study three subclasses of the class of pseudocompact spaces. We answer two open questions concerning cellular-compact spaces and another concerning cellular-Lindelöf 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 L OT S is metrizable.

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