We construct a family of Hausdorff spaces such that every finite product ofspaces in the family (possibly with repetitions) is CLP-compact, while theproduct of all spaces in the family is non-CLP-compact. Our example will yielda single Hausdorff space $X$ such that every finite power of $X$ isCLP-compact, while no infinite power of $X$ is CLP-compact. This answers aquestion of Stepr\={a}ns and \v{S}ostak.
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机译：我们构造了一个Hausdorff空间族，使得该族中每个空间的有限乘积（可能带有重复）都是CLP紧凑的，而该族中所有空间的乘积都是非CLP紧凑的。我们的示例将产生单个Hausdorff空间$ X $，使得$ X $的每个有限幂都是CLP紧凑的，而$ X $的无穷幂是CLP紧凑的。这回答了Stepr \ = {a} ns和\ v {S} ostak的问题。
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