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

Name: A non-CLP-compact product space whose finite subproducts are CLP-compact
Creator: Andrea Medini
Keywords: logic, 101013 Mathematische Logik, General Topology (math.GN), Infinite products, Clopen sets, 01 natural sciences, 101013 Mathematical logic, 101022 Topology, FOS: Mathematics, CLP-compactness

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Dec 2010Embargo end date: 01 Jan 2010 Austria English Publisher:Elsevier BVJournal:Topology and its Applications, volume 157, pages 2,829-2,833 (issn: 0166-8641,

Authors: Andrea Medini;

doi: 10.1016/j.topol.2010.09.001 , 10.48550/arxiv.1005.1974

arXiv: http://arxiv.org/abs/1005.1974

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

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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 Stepr��ns and ��ostak.

8 pages

Country

Austria

Related Organizations

University of Wisconsin–Oshkosh
United States
University of Vienna
Austria

Keywords

logic, 101013 Mathematische Logik, General Topology (math.GN), Infinite products, Clopen sets, 101013 Mathematical logic, 101022 Topology, FOS: Mathematics, CLP-compactness, Geometry and Topology, 101022 Topologie, general topology, Mathematics - General Topology

1 Research products, page 1 of 1

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