Tkachuk and Wilson proved that a regular first countable cellular-compact space has cardinality not exceeding the continuum. In the same paper they asked if this result continues to hold for Hausdorff spaces. Xuan and Song considered the same notion and asked if every cellular-compact space is weakly Lindelof. We answer the last question for first countable spaces. As a byproduct of this result, we present a somewhat different proof of Tkachuk and Wilson theorem, valid for the wider class of Urysohn spaces. The result actually holds for a class of spaces in between cellular-compact and cellular-Lindelof. We conclude with some comments on the cardinality of a weakly linearly Lindelof space.

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关于蜂窝紧凑型和相关空间

Tkachuk 和 Wilson 证明了规则的第一可数元胞紧空间的基数不超过连续统。在同一篇论文中，他们询问这个结果是否继续适用于 Hausdorff 空间。宣和宋考虑了同样的想法，问是否每个细胞致密空间都是弱林德洛夫。我们回答第一个可数空间的最后一个问题。作为这个结果的副产品，我们提出了一个有点不同的 Tkachuk 和 Wilson 定理的证明，它适用于更广泛的 Urysohn 空间类别。结果实际上适用于蜂窝紧凑和蜂窝-林德洛夫之间的一类空间。我们最后对弱线性林德洛夫空间的基数进行了一些评论。