Bornological convergence and separation in (L,M)-fuzzy bornological vector spaces

Document Type : Research Paper

Authors

College of Science, North China University of Technology

Abstract

In this paper, the notions of (L,M)-fuzzy bornological convergence and separation in (L,M)-fuzzy bornological vector spaces are introduced. Some properties of (L,M)-fuzzy bornological convergence and separation are discussed. The relationships between (L,M)-fuzzy bornologial convergence and separation in (L,M)-fuzzy bornological vector spaces are proposed. Moreover, the relationships of bornological convergence and separation between the framework of (L,M)-fuzzy bornological vector spaces and L-bornological vector spaces are discussed.

Keywords

Main Subjects

References

[1] M. Abel, A. ˇSostak, Towards the theory of L-bornological spaces, Iranian Journal of Fuzzy Systems, 8(1) (2011),
19-28. https://doi.org/10.22111/ijfs.2011.233
[2] G. Beer, S. Levi, Gap excess and bornological convergence, Set-Valued and Variational Analysis, 16 (2008), 489-506.
https://doi.org/10.1007/s11228-008-0086-8
[3] G. Beer, S. Levi, Strong uniform continuity, Journal of Mathematical Analysis and Applications, 350 (2009), 568-
589. https://doi.org/10.1016/j.jmaa.2008.03.058
[4] G. Beer, S. Levi, Total boundedness and bornology, Topology and Its Applications, 156 (2009), 1271-1288. https:
//doi.org/10.1016/j.topol.2008.12.030
5] G. Beer, S. Naimpally, J. Rodr´ıguez-L´opez, S-topologies and bounded convergences, Journal of Mathematical Analysis
and Applications, 339 (2008), 542-552. https://doi.org/10.1016/j.jmaa.2007.07.010
[6] A. Caserta, G. Di Maio, L. Hol, Arzels theorem and strong uniform convergence on bornologies, Journal of Mathematical Analysis and Applications, 371 (2010), 384-392. https://doi.org/10.1016/j.jmaa.2010.05.042
[7] J. X. Fang, C. H. Yan, L-fuzzy topological vector spaces, The Journal of Fuzzy Mathematics, 5(1) (1997), 133-144.
[8] Y. Gao, B. Pang, Subcategories of the category of ⊤-convergence spaces, Hacettepe Journal of Mathematics and
Statistics, 53(1) (2024), 88-106. https://doi.org/10.15672/hujms.1205089
[9] G. Gierz et al., A compendium of continuous lattices, Springer Verlag, Berlin, 1980.
[10] H. Hogle-Nled, Bornology and functional analysis, North-Holland Mathematics Studies, Amsterdam, 26 (1977).
[11] S. T. Hu, Boundedness in a topological space, Journal de Math´ematiques Pures et Appliqu´ees, 78 (1949), 287-320.
[12] S. T. Hu, Introduction to general topology, Holden-Day, San-Francisko, 1996.
[13] Z. Y. Jin, C. H. Yan, Induced L-bornological vector spaces and L-Mackey convergence, Journal of Intelligent and
Fuzzy Systems, 40 (2021), 1277-1285. https://doi.org/10.3233/jifs-201599
[14] Z. Y. Jin, C. H. Yan, Fuzzifying bornological linear spaces, Journal of Intelligent and Fuzzy Systems, 42(3) (2022),
2347-2358. https://doi.org/10.3233/JIFS-211644
[15] A. Lechicki, S. Levi, A. Spakowski, Bornological convergence, Journal of Mathematical Analysis and Applications,
297 (2004), 751-770. https://doi.org/10.1016/j.jmaa.2004.04.046
[16] C. Liang, F. G. Shi, J. Wang, (L,M)-fuzzy bornological spaces, Fuzzy Sets and Systems, 467 (2023), 108496.
https://doi.org/10.1016/j.fss.2023.02.017
[17] S. A. Naimpally, B. D. Warrack, Proximity spaces, Cambridge Tracts in Mathematics, 59, Cambridge, 1970.
[18] S. Os¸caˇg, Bornologies and bitopological function spaces, Filomat, 27(7) (2013), 1345-1349. https://doi.org/10.
2298/FIL1307345O
[19] J. Paseka, S. A. Solovyov, M. Stehl´ık, On the category of lattice-valued bornological vector spaces, Journal of
Mathematical Analysis and Applications, 419 (2014), 138-155. https://doi.org/10.1016/j.jmaa.2014.04.033
[20] S. E. Rodabaugh, Powerset operator foundations for poslat fuzzy set theories and topologies, in: U. H¨ohle,
S.E. Rodabaugh(Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Handbook Series,
Kluwer Academic Publishers, Boston, Dordrecht, London, 2 (1999), 91-116. https://doi.org/10.1007/
978-1-4615-5079-2{_}3
[21] H. H. Schaefar, Topological vector spaces, Springer Verlag, 1970.
[22] Y. Shen, C. H. Yan, Fuzzifying bornologies induced by fuzzy pseudo-norms, Fuzzy Sets and Systems, 467 (2023),
108436. https://doi.org/10.1016/j.fss.2022.11.007
[23] F. G. Shi, Theory of Lβ-nested sets and Lα-nested sets and its applications, Fuzzy Systems and Mathematics, 4
(1995), 65-72, (in Chinese).
[24] A. ˇSostak, I. Ul¸jane, L-valued bornologies on powersets, Fuzzy Sets and Systems, 294 (2016), 93-104. https:
//doi.org/10.1016/j.fss.2015.07.016
[25] A. ˇSostak, I. Ul¸jane, Bornological structures on many-valued sets, Rad Hazu. Matematiˇcke Znanosti, 532, 56(21)
(2017), 143-168. https://doi.org/10.21857/90836cdw6y
[26] I. Ul¸jane, A. ˇSostak, M-bornologies on L-valued sets, Advances in Intelligent Systems and Computing, 643 (2018),
450-462. https://doi.org/10.1007/978-3-319-66827-7{_}41
[27] T. Vroegrijk, Uniformizable and realcompact bornological universes, Applied General Topology, 10(2) (2009), 277-
287. https://doi.org/10.4995/agt.2009.1740
[28] H. Zhang, H. P. Zhang, The construction of I-bornological vector spaces, Journal of Mathematical Research with
Applications, 36(2) (2016), 223-232. https://doi.org/10.3770/j.issn:2095-2651.2016.02.011
Iranian Journal of Fuzzy Systems
Volume 22, Issue 1
January and February 2025
Pages 23-33

Files

Share

How to cite

Statistics