Set-theoretic constructions of nonshrinking open covers |
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Authors: | Amer Bešlagić Mary Ellen Rudin |
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Affiliation: | Mathematics Department, University of Wisconsin-Madison, Madison, WI 53706, USA |
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Abstract: | A family {Mα|α?A} is a shrinking of a cover {Oα|α?A} of a topological space if {Mα|α?A} also covers and Mα?Oα for all α?A.?++ implies that there is a normal space such that every increasing open cover of it has a clopen shrinking but there is an open cover having no closed shrinking.? implies that there is a P-space (i.e. a space having a normal product with every metric space), which has an increasing open cover having no closed shrinking. This space is used in [17] to show that any space which has a normal product with every P-space is metrizable. |
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Keywords: | 54D18 54A35 03E45 |
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