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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (2): 92-97.doi: 10.6040/j.issn.1671-9352.0.2021.099

• • 上一篇    

理想遗传不可解空间

卢诗展1,刘媛媛2,程龙生1*   

  1. 1. 南京理工大学经济管理学院, 江苏 南京 210094;2. 郑州卫生健康职业学院, 河南 郑州 450000
  • 发布日期:2022-01-07
  • 作者简介:卢诗展(1987— ), 男, 博士, 讲师, 研究方向为拓扑学、数据挖掘. E-mail:lushizhan20140910@126.com *通信作者简介:程龙生(1964— ), 男, 博士, 教授, 研究方向为统计学、数据挖掘. E-mail:chenglongshengnj@163.com

Ideal hereditary irresolvable spaces

LU Shi-zhan1, LIU Yuan-yuan2, CHENG Long-sheng1*   

  1. 1. School of Economics and Management, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China;
    2. Zhengzhou Health Vocational College, Zhengzhou 450000, Henan, China
  • Published:2022-01-07

摘要: 研究了理想遗传不可解空间的一些空间性质,并证明了如果一个理想拓扑空间是理想Alexandroff空间,则理想遗传不可解空间和理想scattered空间是等价的。

关键词: 理想不可解, 理想遗传不可解, 拓扑和, 理想scattered

Abstract: Some space properties of the ideal hereditary irresolvable space are researched. It is proved that an ideal hereditary irresolvable space and an ideal scattered space are equivalent, if they are ideal Alexandroff topological spaces.

Key words: ideal irresolvable, ideal hereditary irresolvable, topological sums, ideal scattered

中图分类号: 

  • O189
[1] LU Ling, JOANNOPOULOS J D, SOLJACIC M. Topological photonics[J]. Nature Photonics, 2014, 8(11):821-829.
[2] KHANIKAEV A B, SHVETS G. Two-dimensional topological photonics[J]. Nature Photonics, 2017, 11(12):763-773.
[3] ZHANG Haidong, SHU Lan, LIAO Shilong. Topological structures of interval-valued hesitant fuzzy rough set and its application[J]. Journal of Intelligent & Fuzzy Systems, 2016, 30(2):1029-1043.
[4] EGENHOFER M J, FRANZOSA R D. Point-set topological spatial relations[J]. International Journal of Geographical Information System, 1991, 5(2):161-174.
[5] RIAZ M, DAVVAZ B, FAKHAR A, et al. Hesitant fuzzy soft topology and its applications to multi-attribute group decision-making[J]. Soft Computing, 2020, 24(21):16269-16289.
[6] BHATTACHARYA S, LIKHACHEV M, KUMAR V. Topological constraints in search-based robot path planning[J]. Auton Robot, 2012, 33(3):273-290.
[7] JANKOVIC D S, HAMLETT T R. New topologies from old via ideals[J]. The American Mathematical Monthly, 1990, 97(4):295-310.
[8] CATALAN G T, PADUA R N, BALDADO Jr. M P. On β-open sets and ideals in topological spaces[J]. European Journal of Pure and Applied Mathematics, 2019, 12(3):893-905.
[9] KOAM A N A, IBEDOU I, ABBAS S E. Fuzzy ideal topological spaces[J]. Journal of Intelligent & Fuzzy Systems, 2019, 36(6):5919-5928.
[10] GANESAN S. Micro ideal generalized closed sets in micro ideal topological spaces[J]. The International Journal of Analytical and Experimental Modal Analysis, 2020, 7(5):1417-1437.
[11] CAI Zhangyong, ZHENG Dingwei, LI Zhaowen, et al. I -separability on ideal topological spaces[J]. Journal of Advanced Research in Pure Mathematics, 2011, 3(4):85-91.
[12] EKICI E. On I -Alexandroff and I g-Alexandroff ideal topological spaces[J]. Filomat, 2011, 25(4):99-108.
[13] MUKHERJEE M N, ROY B, SEN R. On extensions of topological spaces in terms of ideals[J]. Topology and Its Applications, 2007, 154(18):3167-3172.
[14] LI Zhaowen, LU Shizhan. On I -scattered space[J]. Bulletin of the Korean Mathematical Society, 2014, 51(3):667-680.
[15] HEWITT E. A problem of set-theoretic topology[J]. Duke Mathematical Journal, 1943, 10(2):309-333.
[16] PAVLOV O. On resolvability of topological spaces[J]. Topology and Its Applications, 2002, 126(2):37-47.
[17] COMFORT W W, MASAVEU O, ZHOU Hao. Resolvability in topology and in topological groups[J]. Annals of the New York Academy of Sciences, 1995, 767(1):17-27.
[18] LINDNER S. Resolvability properties of similar topologies[J]. Bulletin of the Australian Mathematical Society, 2015, 1(3):1-8.
[19] DONTCHEV J, GANSTER M, ROSE D. Ideal resolvability[J]. Topology and Its Applications, 1999, 93(1):1-16.
[20] WAGNER-BOJAKOWSKA E. Resolvability of I-density topology[J]. Zeszyty Naukowe Wyzsz ej Szkoy Informatyki, 2001, 1(1):35-37.
[21] 高国士. 拓扑空间论[M]. 北京: 科学出版社, 2008: 7-20. GAO Guoshi. Topological space theory[M]. Beijing: Science Press, 2008: 7-20.
[22] HAYASHI E. Topologies defined by local properties[J]. Mathematische Annalen, 1964, 156(3):205-215.
[23] LI Zhaowen, LIN Funing. On I -baire spaces[J]. Filomat, 2013, 27(2):301-310.
[24] HATIR E, KESKIN A, NOIRI T. A note on strong β-I -sets and strongly β-I -continuous functions[J]. Acta Mathematica Hungarica, 2005, 108(1):87-94.
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