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

2010/05/11 by Andrea Medini, Medini, Andrea
Mathematics · #FOS: Mathematics #General Topology (math.GN) #math.GN

paper · pdf · doi:10.48550/arxiv.1005.1974

8 pages

arxiv created 2011/12/04 · arxiv updated 2011/12/06

Abstract

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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