International Journal of Neutrosophic Science

Journal DOI

https://doi.org/10.54216/IJNS

Submit Your Paper

2690-6805ISSN (Online) 2692-6148ISSN (Print)

Volume 24 , Issue 4 , PP: 126-132, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

Convergence of Filters on Bornological Vector Spaces and Neutrosophic Filters

Fatma Al-Basri 1 * , Asawer Khdeidan 2

  • 1 Department of Mathematics, University of Al-Qadisiyah, 58001, Iraq - (fatma.Albasri@qu.edu.iq)
  • 2 Department of Mathematics, University of Al-Qadisiyah, 58001, Iraq - (asawer.jabbar@qu.edu.iq)
  • Doi: https://doi.org/10.54216/IJNS.240409

    Received: October 23, 2023 Revised: February 13, 2024 Accepted: May 28, 2024
    Abstract

    In this research, we construct new type of convergence of bornological vector spaces called convergence of filters through using conception bounded sets. As well, we have considered several characteristics of these concepts like Fréchet filter associated with sequence, filter that has a unique limit and ultra-filter which is very useful in the study of neutrosophic topological spaces and neutrosophic filters.

    Keywords :

    Convergence , Bornology , Filter , Fré , chet filter , neutrosophic topology , neutrosophic filter.

    References

     

    [1]        Hogbe-Nlend H. Bornologies and functional analysis: introductory course on the theory of duality topology-bornology and its use in functional analysis. Elsevier; 1977.

    [2]        Attouch H, Lucchetti R, Wets RJ-B. The topology of the ρ-Hausdorff distance. Annali Di Matematica Pura Ed Applicata 1991;160:303–20.

    [3]        Beer G. More about metric spaces on which continuous functions are uniformly continuous. Bulletin of the Australian Mathematical Society 1986;33:397–406.

    [4]        Beer G. On metric boundedness structures. Set-Valued Analysis 1999;7:195–208.

    [5]        Beer G. Embeddings of bornological universes. Set-Valued Analysis 2008;16:477–88.

    [6]        Lechicki A, Levi S, Spakowski A. Bornological convergences. Journal of Mathematical Analysis and Applications 2004;297:751–70.

    [7]        Al-Basri FKM. On Complete Convex Bornological Vector Spaces. Al-Qadisiyah Journal of Pure Science 2014;19.

    [8]        Ayaseh D, Ranjbari A. Bornological convergence in locally convex cones. Mediterranean Journal of Mathematics 2016;13:1921–31.

    [9]        Aydemir S, Albayrak H. Filter bornological convergence in topological vector spaces. Filomat 2021;35:3733–43.

    [10]      Al-Basri FK. Sequentially Bornological Compact Space. AL-Qadisiyah Journal of Pure Science 2018;23:293–8.

    [11]      Bergelson V. Ultrafilters, IP sets, dynamics, and combinatorial number theory. Ultrafilters across Mathematics 2010;530:23–47.

    [12]      Stadler BMR, Stadler PF, Wagner GP, Fontana W. The topology of the possible: Formal spaces underlying patterns of evolutionary change. Journal of Theoretical Biology 2001;213:241–74.

    [13] F. Smarandache, Neutrosophy and neutrosophic logic, first international conference on neutrosophy, neu- trosophic logic, set, probability, and statistics, University of New Mexico, Gallup, NM 87301, USA(2002).

    [14] A. Salama and S. AL-Blowi, Neutrosophic Set and Neutrosophic Topological Spaces, IOSR Journal of Math-

    ematics, 3(4) (2012), 31–35.

    [15] A. Salama and S. AL-Blowi, Generalized neutrosophic set and generalized neutrosophic topological spaces, Computer Science and Engineering, 2(7) (2012), 129–132

    Cite This Article As :
    Al-Basri, Fatma. , Khdeidan, Asawer. Convergence of Filters on Bornological Vector Spaces and Neutrosophic Filters. International Journal of Neutrosophic Science, vol. , no. , 2024, pp. 126-132. DOI: https://doi.org/10.54216/IJNS.240409
    Al-Basri, F. Khdeidan, A. (2024). Convergence of Filters on Bornological Vector Spaces and Neutrosophic Filters. International Journal of Neutrosophic Science, (), 126-132. DOI: https://doi.org/10.54216/IJNS.240409
    Al-Basri, Fatma. Khdeidan, Asawer. Convergence of Filters on Bornological Vector Spaces and Neutrosophic Filters. International Journal of Neutrosophic Science , no. (2024): 126-132. DOI: https://doi.org/10.54216/IJNS.240409
    Al-Basri, F. , Khdeidan, A. (2024) . Convergence of Filters on Bornological Vector Spaces and Neutrosophic Filters. International Journal of Neutrosophic Science , () , 126-132 . DOI: https://doi.org/10.54216/IJNS.240409
    Al-Basri F. , Khdeidan A. [2024]. Convergence of Filters on Bornological Vector Spaces and Neutrosophic Filters. International Journal of Neutrosophic Science. (): 126-132. DOI: https://doi.org/10.54216/IJNS.240409
    Al-Basri, F. Khdeidan, A. "Convergence of Filters on Bornological Vector Spaces and Neutrosophic Filters," International Journal of Neutrosophic Science, vol. , no. , pp. 126-132, 2024. DOI: https://doi.org/10.54216/IJNS.240409