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山东大学学报(理学版) ›› 2016, Vol. 51 ›› Issue (2): 114-118.doi: 10.6040/j.issn.1671-9352.0.2014.486

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模糊化拓扑空间的刻画

杨小飞   

  1. 西安工程大学理学院, 陕西 西安 710048
  • 收稿日期:2014-11-04 出版日期:2016-02-16 发布日期:2016-03-11
  • 作者简介:杨小飞(1982— ),男,博士,讲师,研究方向为格上拓扑学. E-mail:yangxiaofei2002@163.com
  • 基金资助:
    国家自然科学基金资助项目(11501435);陕西省教育厅资助项目(2013JK0568);西安工程大学博士科研启动费(BS1319)

Characterization of L-fuzzifying topological spaces

YANG Xiao-fei   

  1. College of Science, Xian Polytechnic University, Xian 710048, Shaanxi, China
  • Received:2014-11-04 Online:2016-02-16 Published:2016-03-11

摘要: 给出模糊化拓扑滤子收敛空间的定义,证明了模糊化拓扑滤子收敛空间和模糊化拓扑空间在范畴意义下是同构的,并且讨论了和其它极限结构的关系。模糊化拓扑滤子收敛空间和模糊化拓扑网收敛空间是匹配的。

关键词: 模糊化拓扑空间, 模糊化拓扑滤子收敛空间, 同构, 模糊化拓扑网收敛空间

Abstract: The concept of fuzzifying topological filter-convergence spaces is introduced, and then it is proved that fuzzifying topological filter-convergence spaces are categorically isomorphic to L-fuzzifying topological spaces. The relationship between fuzzifying topological filter-convergence spaces and other limit structures is established. Finally, it is shown that fuzzifying topological filter-convergence theory is compatible with fuzzifying topological net-convergence theory.

Key words: fuzzifying topological filter-convergence space, L-fuzzifying topological space, isomorphism, fuzzifying topological net-convergence space

中图分类号: 

  • O189.1
[1] HÖHLE U. Upper semicontinuous fuzzy sets and applications[J]. Journal of Mathematical Analysis and Applications, 1980, 78(2):659-674.
[2] YING Mingsheng. A new approach for fuzzy topology(I)[J]. Fuzzy Sets and Systems, 1991, 39(3):303-321.
[3] ZHANG Dexue. L-Fuzzifying topologies as L-topologies[J]. Fuzzy Sets and Systems, 2002, 125(2):135-144.
[4] XU Luoshan. Characterizations of fuzzifying topologies by some limit structures[J]. Fuzzy Sets and Systems, 2001, 123(2):169-176.
[5] 褚晓清,方进明,张虎.模糊化Cook-Fisher对角条件及其应用[J]. 模糊系统与数学,2012, 26(5):1-5. CHU Xiaoqing, FANG Jingming, ZHANG Hu. Fuzzifying Cook-Fischer diagonal condition and its applications[J]. Fuzzy Systems and Mathematics, 2012, 26(5):1-5.
[6] JÄGER G. A category of L-fuzzy convergence spaces[J]. Quaest Math, 2001, 24(4):501-517.
[7] 李令强.多值收敛,多值拓扑和多值序结构[D].成都:四川大学,2008. LI Lingqiang. Many-valued convergence, many-valued topology, many-valued order structure[D]. Chengdou: Sichuan University, 2008.
[8] PANG Bin, FANG Jinming. L-fuzzy Q-convergence structures[J]. Fuzzy Sets and Sestems, 2011, 182(1):53-65.
[9] YAO Wei. Moore-Smith convergence in(L,M)-fuzzy topology[J]. Fuzzy Sets and Sestems, 2012, 190:47-62.
[10] YAO Wei, LU Lingxia. Moore-smith convergence in L-fuzzifying topological spaces[J]. Journal of Mathematical Research & Exposition, 2011, 31(5):770-780.
[11] KELLEY J. General topology[M]. New York: Van Nostrand Reinhold Co, 1955.
[12] PREUSS G. Foundation of topology[M]. London: Kluwer Academic Publishers, 2002.
[13] ENGELKING R. General topology[M]. Berlin: Heldermann Verlag, 1989.
[14] YANG Xiaofei, LI Shenggang. Net-theoretical convergence in(L,M)-fuzzy cotopological spaces[J]. Fuzzy Sets and Systems, 2012, 204:53-65.
[15] LIU Yingming, LUO Maokang. Fuzzy topology[M]. Singapore: World Scientific Publishing, 1997.
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