Previous |  Up |  Next


Title: HC-convergence theory of $L$-nets and $L$-ideals and some of its applications (English)
Author: Nouh, A. A.
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 128
Issue: 4
Year: 2003
Pages: 349-366
Summary lang: English
Category: math
Summary: In this paper we introduce and study the concepts of $\operatorname{\text{HC}}$-closed set and $\operatorname{\text{HC}}$-limit ($\operatorname{\text{HC}}$-cluster) points of $L$-nets and $L$-ideals using the notion of almost $N$-compact remoted neighbourhoods in $L$-topological spaces. Then we introduce and study the concept of $\operatorname{\text{HL}}$-continuous mappings. Several characterizations based on $\operatorname{\text{HC}}$-closed sets and the $\operatorname{\text{HC}}$-convergence theory of $L$-nets and $L$-ideals are presented for $\operatorname{\text{HL}}$-continuous mappings. (English)
Keyword: $L$-topology
Keyword: remoted neighbourhood
Keyword: almost $N$-compactness
Keyword: $\operatorname{\text{HC}}$-closed set
Keyword: $\operatorname{\text{HL}}$-continuity
Keyword: $L$-net
Keyword: $L$-ideal
Keyword: $\operatorname{\text{HC}}$-convergence theory
MSC: 54A20
MSC: 54A40
MSC: 54C08
MSC: 54H12
idZBL: Zbl 1053.54505
idMR: MR2032473
DOI: 10.21136/MB.2003.134000
Date available: 2009-09-24T22:10:42Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] S. L. Chen: Theory of $L$-fuzzy $H$-sets.Fuzzy Sets and Systems 51 (1992), 89–94. Zbl 0788.54004, MR 1187375
Reference: [2] S. L. Chen, X. G. Wang: $L$-fuzzy $N$-continuous mappings.J. Fuzzy Math. 4 (1996), 621–629. MR 1410635
Reference: [3] S. L. Chen, S. T. Chen: A new extension of fuzzy convergence.Fuzzy Sets and Systems 109 (2000), 199–204. MR 1719626
Reference: [4] S. Dang, A. Behera: Fuzzy $H$-continuous functions.J. Fuzzy Math. 3 (1995), 135–145. MR 1322865
Reference: [5] J. M. Fang: Further characterizations of $L$-fuzzy $H$-set.Fuzzy Sets and Systems 91 (1997), 355–359. Zbl 0917.54011, MR 1481282, 10.1016/S0165-0114(96)00153-4
Reference: [6] M. Han, M. Guangwu: Almost $N$-compact sets in $L$-fuzzy topological spaces.Fuzzy Sets and Systems 91 (1997), 115–122. MR 1481275, 10.1016/S0165-0114(96)00123-6
Reference: [7] U. Höhle, S. E. Rodabaugh: Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory.The Handbooks of Fuzzy Series 3, Kluwer Academic Publishers, Dordrecht, 1999. MR 1788899
Reference: [8] Y. M. Liu, M. K. Luo: Fuzzy Stone-Čech-type compactifications.Fuzzy Sets and Systems 33 (1989), 355–372. MR 1033881
Reference: [9] Y. M. Liu, M. K. Luo: Separations in lattice-valued induced spaces.Fuzzy Sets and Systems 36 (1990), 55–66. MR 1063271, 10.1016/0165-0114(90)90078-K
Reference: [10] P. E. Long, T. R. Hamlett: $H$-continuous functions.Bolletino U. M. I. 11 (1975), 552–558. MR 0383336
Reference: [11] M. N. Mukherjee, S. P. Sinha: Almost compact fuzzy sets in fuzzy topological spaces.Fuzzy Sets and Systems 48 (1990), 389–396. MR 1083070
Reference: [12] G. J. Wang: A new fuzzy compactness defined by fuzzy nets.J. Math. Anal. Appl. 94 (1983), 59–67. Zbl 0512.54006, MR 0701446
Reference: [13] G. J. Wang: Generalized topological molecular lattices.Scientia Sinica (Ser. A) 27 (1984), 785–793. Zbl 0599.54005, MR 0795162
Reference: [14] G. J. Wang: Theory of $L$-Fuzzy Topological Spaces.Shaanxi Normal University Press, Xi’an, 1988.
Reference: [15] Z. Q. Yang: Ideal in topological molecular lattices.Acta Mathematica Sinica 29 (1986), 276–279. MR 0855716
Reference: [16] D. S. Zhao: The $N$-compactness in $L$-fuzzy topological spaces.J. Math. Anal. Appl. 128 (1987), 64–79. Zbl 0639.54006, MR 0915967, 10.1016/0022-247X(87)90214-9


Files Size Format View
MathBohem_128-2003-4_2.pdf 375.9Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo