| 伏文清,李生刚.关于Hutton定理的一个注[J].数学研究及应用,2008,28(2):429~434 |
| 关于Hutton定理的一个注 |
| A Note to Hutton's Theorem |
| 投稿时间：2006-06-20 修订日期：2007-07-13 |
| DOI：10.3770/j.issn:1000-341X.2008.02.025 |
| 中文关键词: $L$-单位区间 通常拓扑 保并 保交. |
| 英文关键词:$L$-unit interval ordinary topology meet-preserving mapping join-preserving mapping. |
| 基金项目:国家自然科学基金(No.10271069). |
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| 摘要点击次数: 2576 |
| 全文下载次数: 2004 |
| 中文摘要: |
| 本文证明了存在一个一一对应$\varphi: {\cal J}\cup{\cal J}'\longrightarrow\delta\cup\delta'$,它满足: \ \ (1) $\varphi|{\cal J}: ({\cal J},\subset)\longrightarrow(\delta,\leq)$是frame同构. \ \ (2) $\varphi|{\cal J}': ({\cal J}',\subset)\longrightarrow(\delta',\leq)$是coframe同构. |
| 英文摘要: |
| It is proved in this paper that there is a bijection $\varphi$ from ${\cal J}\cup{\cal J}'$ to $\delta\cup\delta'$ which satisfies: (1)~$\varphi|{\cal J}: ({\cal J},\subset)\longrightarrow(\delta,\leq)$ is a frame isomorphism; (2)~$\varphi|{\cal J}': ({\cal J}',\subset)\longrightarrow(\delta',\leq)$ is a coframe isomorphism, where ${\cal J}$ is the ordinary topology on $[0,1]$, $\delta$ is the ordinary $L$-topology on $L$-unit interval $I(L)$, and $L$ is a frame with an order-reversing involution. This result improves Theorem 3 in Hutton's paper. |
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