A non-CLP-compact product space whose finite subproducts are CLP-compact

We construct a family of Hausdorff spaces such that every finite product of spaces in the family (possibly with repetitions) is CLP-compact, while the product of all spaces in the family is non-CLP-compact. Our example will yield a single Hausdorff space $X$ such that every finite power of $X$ is CLP-compact, while no infinite power of $X$ is CLP-compact. This answers a question of Steprāns and Šostak.

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