On Products of Property b1 |
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Authors: | Jianjun WANG Peiyong ZHU |
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Institution: | School of Mathematical Sciences, University of Electronic Science and Technology of China,Sichuan 611731, P. R. China |
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Abstract: | In this note,we present that:(1) Let X=σ{Xα:α∈A} be |A|-paracompact (resp.,hereditarily |A|-paracompact).If every finite subproduct of {Xα:α∈A} has property b1 (resp.,hereditarily property b1),then so is X.(2) Let X be a P-space and Y a metric space.Then,X×Y has property b1 iff X has property b1.(3) Let X be a strongly zero-dimensional and compact space.Then,X×Y has property b1 iff Y has property b1. |
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Keywords: | σ-product Tychonoff products property b1 hereditarily property b1 |
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