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| L-预拓扑空间中的近似L-开集及相关的连通性和范畴性质 | |
| 引用本文： | 杨婷,李生刚,伏文清.L-预拓扑空间中的近似L-开集及相关的连通性和范畴性质[J].模糊系统与数学,2012,26(1):1-7. |
| 作者姓名： | 杨婷 李生刚 伏文清 |
| 作者单位： | 1. 陕西师范大学数学与信息科学学院,陕西西安710062;石河子大学理学院数学系,新疆石河子832000 2. 陕西师范大学数学与信息科学学院,陕西西安,710062 3. 西安工业大学数理系,陕西西安,710032 |
| 基金项目： | 国家自然科学基金，陕西省自然科学基金，陕西省教育厅专项科研计划项目 |
| 摘 要： | 研究L-预拓扑空间中L-开集的一些近似形式(其中L是有逆合对应的C-格):θ-L-开集,δ-L-开集,α-L-开集以及β-L-开集。证明了(1)当L的最大元1是并既约元时L-预拓扑空间的连通性、θ-连通性、δ-连通性和α-连通性是等价的;(2)θLTop是LTopsθ、LTop以及LTopθ的反射满子范畴,δLTop是LTopsδ和LTopδ的反射满子范畴;(3)当格L为幂集格时αLTop是LTopsα和LTopα的余反射满子范畴;θLPTop是LPTopsθ、LPTop以及LPTopθ的反射满子范畴,δLPTop是LPTopsδ和LPTopδ的反射满子范畴。 |
| 关 键 词： | L-预拓扑空间 θ-L-开集 δ-L-开集 α-L-开集 连通性 反射子范畴 余反射子范畴 |
Approximate L-open Sets in L-pretopological Spaces and Related Connectedness and Categorical Properties |
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| YANG Ting , LI Sheng-gang , FU We-qing.Approximate L-open Sets in L-pretopological Spaces and Related Connectedness and Categorical Properties[J].Fuzzy Systems and Mathematics,2012,26(1):1-7. | |
| Authors: | YANG Ting LI Sheng-gang FU We-qing |
| Affiliation: | YANG Ting1,2,LI Sheng-gang1,FU We-qing3(1.College of Mathematics and Information Sciences,Shaanxi Normal University,Xi’an 710062,China;2.Department of Mathematics,Shihezi University,Shihezi 832000,China;3.Department of Mathematics and Physics,Xi’an Technological University,Xi’an 710032,China) |
| Abstract: | The paper studies some approximation forms of L-open sets(i.e.θ-L-open sets,δ-L-open sets,α-L-open sets and β-L-open sets) in L-pretopological spaces for L a C-lattice with an order-reversing involution.It is proved that(1) Connectedness,θ-connectedness,δ-connectedness and α-connectedness of an L-pretopological space is the same if 1 is a join irreducible element.(2) θLTop is a reflective subcategory of LTopsθ,LTop and LTopθ,δLTop is a reflective subcategory of LTopsδ,LTopδ,(3) αLTop is a coreflective subcategory of LTopsα and LTopα for L a powerset lattice;θLPTop is a reflective subcategory of LPTopsθ,LPTop and LPTopθ, and δLPTop is a reflective subcategory of LPTopsδ and LTopδ. |
| Keywords: | L-pretopological Space θ-L-open Set δ-L-open Set α-L-open Set Connectedness Reflective Subcategory Coreflective Subcategory |
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