A Note to Hutton's Theorem
Received:June 20, 2006  Revised:July 13, 2007
Key Words: $L$-unit interval   ordinary topology   meet-preserving mapping   join-preserving mapping.  
Fund Project:the National Natural Science Foundation of China (No.10271069).
Author NameAffiliation
FU Wen Qing College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, China 
LI Sheng Gang College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, China 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:1000-341X.2008.02.025
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