JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (2): 92-97.doi: 10.6040/j.issn.1671-9352.0.2021.099
LU Shi-zhan1, LIU Yuan-yuan2, CHENG Long-sheng1*
CLC Number:
[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 Szkoy 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. |
[1] | DUAN Jing-yao. Topological properties analysis of logical metric spaces on the residuated lattice [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(12): 9-16. |
[2] | LIU Yan-fang, WANG Yu-yu. Some notes on E2-term of Adams spectral sequence [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(8): 43-48. |
[3] | GAO Rui-mei, CHU Ying. Freeness of arrangements between the Weyl arrangements of types An-1 and Bn [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 70-75. |
[4] | GUO Hong-feng, LI Yu-si, SUN Wei-hua. D-properties of Finite unions of spaces with point countable weak bases and satisfying open(G) [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 72-76. |
[5] | MA Hai-cheng, LI Sheng-gang. The digraphs representation of finite topologies [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 100-104. |
[6] | . The characteristic polynomials of the graphical arrangements corresponding to the simply-connected polygons [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(10): 72-77. |
[7] | LU Tao, HE Wei. Neighborhood systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 65-69. |
[8] | LU Tao, WANG Xi-juan, HE Wei. The supremum and infimum of partially ordered objects in a topos [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 112-117. |
[9] | ZHANG Guo-fang, YANG Er-guang. Function characterizations of k-semi-stratifiable spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 99-103. |
[10] | YANG Xiao-fei. Characterization of L-fuzzifying topological spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 114-118. |
[11] | LU Tao, WANG Xi-juan, HE Wei. The operator theory on complete partially ordered objects in a topos [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 64-71. |
[12] | LU Tao, WANG Xi-juan, HE Wei. An equivalent characterization of the choice axiom in a Topos [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 54-57. |
[13] | GAO Rui-mei, SUN Yan. Quadratic Gröbner basis and the isomorphism of Orlik-Solomon algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(06): 89-94. |
[14] | GAO Rui-mei. The freeness of Shi-Catalan arrangements of type G2 [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(12): 66-70. |
[15] | LU Han-chuan, LI Sheng-gang. Characterization of bicompletable interval-valued fuzzy quasi-metric spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 72-77. |
|