| 具有性质$b_1$空间的乘积性 |
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| 引用本文： | 王建军,朱培勇.具有性质$b_1$空间的乘积性[J].数学研究及应用,2012,32(2):241-247. |
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| 作者姓名： | 王建军 朱培勇 |
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| 作者单位： | 电子科技大学数学科学学院, 四川 成都 611731;电子科技大学数学科学学院, 四川 成都 611731 |
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| 基金项目： | 国家自然科学基金(Grant Nos.10671134; 11026081). |
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| 摘 要： | 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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| 关 键 词： | σ-product Tychonoff products property b1 hereditarily property b1. |
| 收稿时间： | 2010/7/13 0:00:00 |
| 修稿时间： | 2010/11/20 0:00:00 |
On Products of Property $b_1$ |
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| Jianjun WANG and Peiyong ZHU.On Products of Property $b_1$[J].Journal of Mathematical Research with Applications,2012,32(2):241-247. |
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| Authors: | Jianjun WANG and Peiyong ZHU |
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| Institution: | School of Mathematical Sciences, University of Electronic Science and Technology of China, Sichuan 611731, P. R. China;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 $X$=$\sigma\{X_{\alpha}:\alpha\in A\}$ be $\left| A \right|$-paracompact (resp., hereditarily $\left| A \right|$-paracompact). If every finite subproduct of ${\rm \{ } X\-\alpha: \alpha \in A {\rm \} }$ has property $b_1$ (resp., hereditarily property $b_1$), then so is $X$. (2)~Let $X$ be a P-space and $Y$ a metric space. Then, $X\times Y$ has property $b_1 $ iff $X$ has property $b_1 $. (3)~Let $X$ be a strongly zero-dimensional and compact space. Then, $X\times Y$ has property $b_1 $ iff $Y$ has property $b_1$. |
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| Keywords: | $\sigma$-product Tychonoff products property $b_1$ hereditarily property $b_1$ |
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