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On Products of Property b1
Authors:Jianjun WANG  Peiyong ZHU
Institution:School of Mathematical Sciences, University of Electronic Science and Technology of China,Sichuan 611731, P. R. China
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.
Keywords:σ-product  Tychonoff products  property b1  hereditarily property b1
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