| Stone's representation theorem in fuzzy topology |
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| 作者姓名： | 刘应明 张德学 |
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| 作者单位： | Department of Mathematics，Sichuan University，Chengdu 610064，China Correspondence should be addressed to Liu Yingming，Department of Mathematics，Sichuan University，Chengdu 610064，China Correspondence should be addressed to Liu Yingming |
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| 基金项目： | 国家自然科学基金，国家重点基础研究发展计划(973计划)，the Science Foundation of MOE of China，教育部霍英东教育基金 |
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| 摘 要： | In this paper, a complete solution to the problem of Stone's repesentation theorem in fuzzy topology is given for a class of completely distributive lattices. Precisely, it is proved that if L is a frame such that 0 ∈ L is a prime or 1 ∈ L is a coprime, then the category of distributive lattices is dually equivalent to the category of coherent L-locales and that if L is moreover completely distributive, then the category of distributive lattices is dually equivalent to the category of coherent stratified L-topological spaces.
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Stone’s representation theorem in fuzzy topology |
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| Yingming?LiuEmail author,Dexue?ZhangEmail author.Stone''''s representation theorem in fuzzy topology[J].Science in China(Mathematics),2003,46(6):775-788. |
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| Authors: | Email author" target="_blank">Yingming?LiuEmail author Email author" target="_blank">Dexue?ZhangEmail author |
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| Institution: | Department of Mathematics, Sichuan University, Chengdu 610064, China |
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| Abstract: | In this paper, a complete solution to the problem of Stone's repesentation theorem in fuzzy topology is given for a class of completely distributive lattices. Precisely, it is proved that if L is a frame such that 0 ∈ L is a prime or 1 ∈ L is a coprime, then the category of distributive lattices is dually equivalent to the category of coherent L-locales and that if L is moreover completely distributive, then the category of distributive lattices is dually equivalent to the category of coherent stratified L-topological spaces. |
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| Keywords: | distributive lattice L-topoiogical space Stone's representation theorem frame |
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