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Fuzzifying bornivorous sets of fuzzifying bornological linear spaces

Yıl 2025, , 26 - 37, 28.02.2025

Zhen-yu Jin C. H. Yan

https://doi.org/10.15672/hujms.1264856

Öz

The main purpose of this paper is to introduce a notion of fuzzifying bornivorous sets of fuzzifying bornological linear spaces. In particular, we provide an example of fuzzifying bornivorous sets on a fuzzifying topological linear space with its von Neumann bornology. Furthermore, the description of fuzzifying open sets of fuzzifying bornological linear spaces is showed and its equivalent illustration is discussed as well. In addition, we study the dual relationship of fuzzifying open and close sets. The fuzzifying topological space induced by fuzzifying open sets is also discussed.

Anahtar Kelimeler

fuzzifying bornivorous set fuzzifying bornological linear space fuzzifying open set fuzzifying topological linear space

Destekleyen Kurum

National Natural Science Foundation of China

Proje Numarası

No.:12071225

Kaynakça

  • [1] M. Abel and A. Šostak, Towards the theory of L-bornological spaces, Iran. J. Fuzzy Syst. 8 (1), 19–28, 2011.
  • [2] J. Almeida and L. Barreida, Hausdorff dimension in convex bornological spaces, J. Math. Anal. Appl. 268, 590–601, 2002.
  • [3] G. Beer, S. Naimpally and J. Rodrigues-Lopes, S-topologies and bounded convergences, J. Math. Anal. Appl. 339, 542–552, 2008.
  • [4] G. Beer and S. Levi, Gap, excess and bornological convergence, Set-Valued Anal. 16, 489–506, 2008.
  • [5] G. Beer and S. Levi, Total boundedness and bornology, Topology Appl. 156, 1271–1288, 2009.
  • [6] G. Beer and S. Levi, Strong uniform continuity, J. Math. Anal. Appl. 350, 568–589, 2009.
  • [7] G. Birkhoff, Lattice Theory, AMS, Providence, RI, 1995.
  • [8] A. Caserta, G. Di Maio and L. Holá, Arzelá’s theorem and strong uniform convergence on bornologies, J. Math. Anal. Appl. 371, 384–392, 2010.
  • [9] A. Caserta, G. Di Maio and Lj.D.R. Kocinac, Bornologies, selection principles and function spaces, Topology Appl. 159, 1847–1852, 2012.
  • [10] H. Hogle-Nled, Bornologies and Functional Analysis, North-Holland Publishing Company, 1977.
  • [11] S.T. Hu, Boundedness in a topological space, J. Math. Pures Appl. 28, 287–320, 1949.
  • [12] S.T. Hu, Introduction to general topology, Holden-Day, San-Francisko, 1966.
  • [13] Z. Jin and C. Yan, Induced L-bornological vector spaces and L-Mackey convergence, J. Intell. Fuzzy Systems, 40, 1277–1285, 2021.
  • [14] Z. Jin and C. Yan, Fuzzifying bornological linear spaces, J. Intell. Fuzzy Systems, 42, 2347–2358, 2022.
  • [15] A. Lechicki, S. Levi and A. Spakowski, Bornological convergence, Aust. J. Math. Anal. Appl. 297, 751–770, 2004.
  • [16] R. Meyer, Smooth group representations on bornological vector spaces, Bull. Sci. Math. 128, 127–166, 2004.
  • [17] A.M. Meson and F. Vericat, A functional approach to a topological entropy in bornological linear spaces, J. Dyn. Syst. Geom. Theor. 3, 45–54, 2005.
  • [18] S. Osçaˇg, Bornologies and bitopological function spaces, Filomat 27 (7), 1345–1349, 2013.
  • [19] J. Paseka, S. Solovyov and M. Stehlík, Lattice-valued bornological systems, Fuzzy Sets and Systems, 259, 68–88, 2015.
  • [20] J. Paseka, S. Solovyov and M. Stehlík, On the category of lattice-valued bornological vector spaces, J. Math. Anal. Appl. 419, 138–155, 2014.
  • [21] H.H. Schaefar, Topological Vector Spaces, Springer Verlag, 1970.
  • [22] A. Šostak and I. UI¸jane, L-valued bornologies on powersets, Fuzzy Sets and Systems, 294, 93–104, 2016.
  • [23] D. Qiu, Fuzzifying topological linear spaces, Fuzzy Sets and Systems, 147, 249–272, 2004.
  • [24] I. UI¸jane and A. Šostak, M-bornologies on L-valued Sets, Advances in Intelligent Systems and Computing, Springer, Cham, Warsaw, Poland, 643, 450-462, 2017.
  • [25] C. Yan, Fuzzifying topologies on the space of linear operators, Fuzzy Sets and Systems, 238, 89–101, 2014.
  • [26] M. Ying, A new approach for fuzzy topology (I), Fuzzy Sets and Systems, 39, 303–321, 1991.
  • [27] M. Ying, A new approach for fuzzy topology (II), Fuzzy Sets and Systems, 47, 221–232 1992.
  • [28] D.X. Zhang, Triangular norms on partially ordered sets, Fuzzy Sets and Systems, 153, 195–209, 2005.

Yıl 2025, , 26 - 37, 28.02.2025

Zhen-yu Jin C. H. Yan

https://doi.org/10.15672/hujms.1264856

Öz

Proje Numarası

No.:12071225

Kaynakça

  • [1] M. Abel and A. Šostak, Towards the theory of L-bornological spaces, Iran. J. Fuzzy Syst. 8 (1), 19–28, 2011.
  • [2] J. Almeida and L. Barreida, Hausdorff dimension in convex bornological spaces, J. Math. Anal. Appl. 268, 590–601, 2002.
  • [3] G. Beer, S. Naimpally and J. Rodrigues-Lopes, S-topologies and bounded convergences, J. Math. Anal. Appl. 339, 542–552, 2008.
  • [4] G. Beer and S. Levi, Gap, excess and bornological convergence, Set-Valued Anal. 16, 489–506, 2008.
  • [5] G. Beer and S. Levi, Total boundedness and bornology, Topology Appl. 156, 1271–1288, 2009.
  • [6] G. Beer and S. Levi, Strong uniform continuity, J. Math. Anal. Appl. 350, 568–589, 2009.
  • [7] G. Birkhoff, Lattice Theory, AMS, Providence, RI, 1995.
  • [8] A. Caserta, G. Di Maio and L. Holá, Arzelá’s theorem and strong uniform convergence on bornologies, J. Math. Anal. Appl. 371, 384–392, 2010.
  • [9] A. Caserta, G. Di Maio and Lj.D.R. Kocinac, Bornologies, selection principles and function spaces, Topology Appl. 159, 1847–1852, 2012.
  • [10] H. Hogle-Nled, Bornologies and Functional Analysis, North-Holland Publishing Company, 1977.
  • [11] S.T. Hu, Boundedness in a topological space, J. Math. Pures Appl. 28, 287–320, 1949.
  • [12] S.T. Hu, Introduction to general topology, Holden-Day, San-Francisko, 1966.
  • [13] Z. Jin and C. Yan, Induced L-bornological vector spaces and L-Mackey convergence, J. Intell. Fuzzy Systems, 40, 1277–1285, 2021.
  • [14] Z. Jin and C. Yan, Fuzzifying bornological linear spaces, J. Intell. Fuzzy Systems, 42, 2347–2358, 2022.
  • [15] A. Lechicki, S. Levi and A. Spakowski, Bornological convergence, Aust. J. Math. Anal. Appl. 297, 751–770, 2004.
  • [16] R. Meyer, Smooth group representations on bornological vector spaces, Bull. Sci. Math. 128, 127–166, 2004.
  • [17] A.M. Meson and F. Vericat, A functional approach to a topological entropy in bornological linear spaces, J. Dyn. Syst. Geom. Theor. 3, 45–54, 2005.
  • [18] S. Osçaˇg, Bornologies and bitopological function spaces, Filomat 27 (7), 1345–1349, 2013.
  • [19] J. Paseka, S. Solovyov and M. Stehlík, Lattice-valued bornological systems, Fuzzy Sets and Systems, 259, 68–88, 2015.
  • [20] J. Paseka, S. Solovyov and M. Stehlík, On the category of lattice-valued bornological vector spaces, J. Math. Anal. Appl. 419, 138–155, 2014.
  • [21] H.H. Schaefar, Topological Vector Spaces, Springer Verlag, 1970.
  • [22] A. Šostak and I. UI¸jane, L-valued bornologies on powersets, Fuzzy Sets and Systems, 294, 93–104, 2016.
  • [23] D. Qiu, Fuzzifying topological linear spaces, Fuzzy Sets and Systems, 147, 249–272, 2004.
  • [24] I. UI¸jane and A. Šostak, M-bornologies on L-valued Sets, Advances in Intelligent Systems and Computing, Springer, Cham, Warsaw, Poland, 643, 450-462, 2017.
  • [25] C. Yan, Fuzzifying topologies on the space of linear operators, Fuzzy Sets and Systems, 238, 89–101, 2014.
  • [26] M. Ying, A new approach for fuzzy topology (I), Fuzzy Sets and Systems, 39, 303–321, 1991.
  • [27] M. Ying, A new approach for fuzzy topology (II), Fuzzy Sets and Systems, 47, 221–232 1992.
  • [28] D.X. Zhang, Triangular norms on partially ordered sets, Fuzzy Sets and Systems, 153, 195–209, 2005.
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Zhen-yu Jin

C. H. Yan 0000-0002-6500-7807

Proje Numarası No.:12071225
Erken Görünüm Tarihi 14 Nisan 2024
Yayımlanma Tarihi 28 Şubat 2025
Yayımlandığı Sayı Yıl 2025

Kaynak Göster

APA Jin, Z.-y., & Yan, C. H. (2025). Fuzzifying bornivorous sets of fuzzifying bornological linear spaces. Hacettepe Journal of Mathematics and Statistics, 54(1), 26-37. https://doi.org/10.15672/hujms.1264856
AMA Jin Zy, Yan CH. Fuzzifying bornivorous sets of fuzzifying bornological linear spaces. Hacettepe Journal of Mathematics and Statistics. Şubat 2025;54(1):26-37. doi:10.15672/hujms.1264856
Chicago Jin, Zhen-yu, ve C. H. Yan. “Fuzzifying Bornivorous Sets of Fuzzifying Bornological Linear Spaces”. Hacettepe Journal of Mathematics and Statistics 54, sy. 1 (Şubat 2025): 26-37. https://doi.org/10.15672/hujms.1264856.
EndNote Jin Z-y, Yan CH (01 Şubat 2025) Fuzzifying bornivorous sets of fuzzifying bornological linear spaces. Hacettepe Journal of Mathematics and Statistics 54 1 26–37.
IEEE Z.-y. Jin ve C. H. Yan, “Fuzzifying bornivorous sets of fuzzifying bornological linear spaces”, Hacettepe Journal of Mathematics and Statistics, c. 54, sy. 1, ss. 26–37, 2025, doi: 10.15672/hujms.1264856.
ISNAD Jin, Zhen-yu - Yan, C. H. “Fuzzifying Bornivorous Sets of Fuzzifying Bornological Linear Spaces”. Hacettepe Journal of Mathematics and Statistics 54/1 (Şubat 2025), 26-37. https://doi.org/10.15672/hujms.1264856.
JAMA Jin Z-y, Yan CH. Fuzzifying bornivorous sets of fuzzifying bornological linear spaces. Hacettepe Journal of Mathematics and Statistics. 2025;54:26–37.
MLA Jin, Zhen-yu ve C. H. Yan. “Fuzzifying Bornivorous Sets of Fuzzifying Bornological Linear Spaces”. Hacettepe Journal of Mathematics and Statistics, c. 54, sy. 1, 2025, ss. 26-37, doi:10.15672/hujms.1264856.
Vancouver Jin Z-y, Yan CH. Fuzzifying bornivorous sets of fuzzifying bornological linear spaces. Hacettepe Journal of Mathematics and Statistics. 2025;54(1):26-37.

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