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 LOTS is metrizable.

中文翻译：

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关于细胞致密性和相关性质

我们研究了伪紧空间类的三个子类。我们回答了两个关于元胞紧致空间和另一个关于元胞-Lindelöf 空间的开放性问题，并介绍和研究了弱紧致空间类的其他三个子类，即元胞可数紧致空间类，元胞序列-紧致空间和元胞紧致可计量空间。我们表明，无论蜂窝紧凑可计量的 LOTS 是否可计量，它都与 ZFC 无关。