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Yıl 2025, Erken Görünüm, 1 - 1

Shyamapada Modak Kulchhum Khatun Jiarul Hoque

https://doi.org/10.35378/gujs.967261

Öz

Kaynakça

  • [1] Kuratowski, K., Topology Vol. I, Academic Press, New York, (1966).
  • [2] Husain, T., Topology and Maps, First Edition, Plenum Press, New York and London, (1977).
  • [3] Lahiri, B. K., Das, P., “ and -convergence in topological spaces”, Mathematica Bohemica, 130(2): 153–160, (2005).
  • [4] Modak, S., Hoque, J., Selim, Sk., “Homeomorphic image of some kernels”, Çankaya University Journal of Science and Engineering, 17(1): 052-062, (2020).
  • [5] Noiri, T., Selim, Sk., Modak, S., “Convergence of the associated filters via set-operators”, Çankaya University Journal of Science and Engineering, 17(2): 101-107, (2020).
  • [6] Baran, T. M., Erciyes, A., ‘‘Local T3 constant filter convergence spaces’’, Gazi University Journal of Science, 33(2): 446-454, (2020).
  • [7] Bourbaki, N., “Elements of Mathematics General Topology”, Chapters 1-4, Springer, New York, (1989).
  • [8] Joshi, K. D., “Introduction to general topology” Revised ed., Wiley Estern Limited, New Delhi, (1984).
  • [9] Simmons, G. F., “Introduction to Topology and Modern Analysis”, Robert E. Krieger Publishing Company, Florida, (1963).
  • [10] Levine, N., “Semi-open sets and semi-continuity in topological spaces”, The American Mathematical Monthly, 70(1): 36–41, (1963).
  • [11] Mashhour, A. S., El-Monsef, M. E. Abd., El-Deeb, S. N., “On precontinous and weak precontinous mappings”, Proceedings of the Mathematical and Physical Society of Egypt, 53: 47-53, (1982).
  • [12] Ganster, M., “Preopen sets and resolvable spaces”, Kyungpook Mathematical Journal, 27(2): 135-143, (1987).
  • [13] El-Monsef, M. E. Abd., “ -open sets and -continuous mappings”, Bulletin of the Faculty of Science, Assiut University, 12: 77-90, (1983).
  • [14] Andrijević, D., “Semi-preopen sets”, Matematički Vesnik, 38(93): 24-32, (1986).
  • [15] Andrijević, D., “On -open sets”, Matematički Vesnik, 48: 59-64, (1996).
  • [16] Natkaniec, T., “On -continuity and -semicontinuity points”, Mathematica Slovaca, 36(3): 297-312, (1986).
  • [17] Selim, Sk., Noiri, T., Modak, S., “Operators in terms of * and ”, Boletim da Sociedade Paranaense de Matemática, 41(3): 1-7, (2023).
  • [18] Al-Saadi, H., Al-Omari, A., “Some operators in ideal topological spaces”, Missouri Journal of Mathematical Sciences, 30(1): 59-71, (2018).
  • [19] Al-Omari, A., Noiri, T., “On operators in ideal minimal spaces”, Mathematica, 58(81), (1-2): 3-13, (2016).
  • [20] Selim, Sk., Islam, Md. M., Modak, S., “Common properties and approximations of local function and set operator ”, Cumhuriyet Science Journal, 41(2): 360-368, (2020).
  • [21] Al-Omari, A., Noiri, T., “Local closure functions in ideal topological spaces”, Novi Sad Journal of Mathematics, 43(2): 139-149, (2013).
  • [22] Hoque, J., Modak, S., Acharjee, S., “Filter versus ideal on the topological spaces”, Advances in topology and their interdisciplinary applications, Springer, 183-195, (2023).

Characterizations of Filter Convergent in Terms of Ideal

Yıl 2025, Erken Görünüm, 1 - 1

Shyamapada Modak Kulchhum Khatun Jiarul Hoque

https://doi.org/10.35378/gujs.967261

Öz

In this paper, convergences of a filter and a net have been characterized through ideal on topological spaces. Furthermore, we characterized the local function in an ideal topological space in terms of convergence of filter. Using Zorn's Lemma, we have found a maximal element in the collection of all proper ideals on a nonempty set which is called maximal ideal. We provide a convenient characterization of maximal ideals. We also consider simple properties of the image of an ideal, a net and various local functions under a homeomorphism.

Anahtar Kelimeler

Net Filter Ultrafilter Ideal Local Function

Kaynakça

  • [1] Kuratowski, K., Topology Vol. I, Academic Press, New York, (1966).
  • [2] Husain, T., Topology and Maps, First Edition, Plenum Press, New York and London, (1977).
  • [3] Lahiri, B. K., Das, P., “ and -convergence in topological spaces”, Mathematica Bohemica, 130(2): 153–160, (2005).
  • [4] Modak, S., Hoque, J., Selim, Sk., “Homeomorphic image of some kernels”, Çankaya University Journal of Science and Engineering, 17(1): 052-062, (2020).
  • [5] Noiri, T., Selim, Sk., Modak, S., “Convergence of the associated filters via set-operators”, Çankaya University Journal of Science and Engineering, 17(2): 101-107, (2020).
  • [6] Baran, T. M., Erciyes, A., ‘‘Local T3 constant filter convergence spaces’’, Gazi University Journal of Science, 33(2): 446-454, (2020).
  • [7] Bourbaki, N., “Elements of Mathematics General Topology”, Chapters 1-4, Springer, New York, (1989).
  • [8] Joshi, K. D., “Introduction to general topology” Revised ed., Wiley Estern Limited, New Delhi, (1984).
  • [9] Simmons, G. F., “Introduction to Topology and Modern Analysis”, Robert E. Krieger Publishing Company, Florida, (1963).
  • [10] Levine, N., “Semi-open sets and semi-continuity in topological spaces”, The American Mathematical Monthly, 70(1): 36–41, (1963).
  • [11] Mashhour, A. S., El-Monsef, M. E. Abd., El-Deeb, S. N., “On precontinous and weak precontinous mappings”, Proceedings of the Mathematical and Physical Society of Egypt, 53: 47-53, (1982).
  • [12] Ganster, M., “Preopen sets and resolvable spaces”, Kyungpook Mathematical Journal, 27(2): 135-143, (1987).
  • [13] El-Monsef, M. E. Abd., “ -open sets and -continuous mappings”, Bulletin of the Faculty of Science, Assiut University, 12: 77-90, (1983).
  • [14] Andrijević, D., “Semi-preopen sets”, Matematički Vesnik, 38(93): 24-32, (1986).
  • [15] Andrijević, D., “On -open sets”, Matematički Vesnik, 48: 59-64, (1996).
  • [16] Natkaniec, T., “On -continuity and -semicontinuity points”, Mathematica Slovaca, 36(3): 297-312, (1986).
  • [17] Selim, Sk., Noiri, T., Modak, S., “Operators in terms of * and ”, Boletim da Sociedade Paranaense de Matemática, 41(3): 1-7, (2023).
  • [18] Al-Saadi, H., Al-Omari, A., “Some operators in ideal topological spaces”, Missouri Journal of Mathematical Sciences, 30(1): 59-71, (2018).
  • [19] Al-Omari, A., Noiri, T., “On operators in ideal minimal spaces”, Mathematica, 58(81), (1-2): 3-13, (2016).
  • [20] Selim, Sk., Islam, Md. M., Modak, S., “Common properties and approximations of local function and set operator ”, Cumhuriyet Science Journal, 41(2): 360-368, (2020).
  • [21] Al-Omari, A., Noiri, T., “Local closure functions in ideal topological spaces”, Novi Sad Journal of Mathematics, 43(2): 139-149, (2013).
  • [22] Hoque, J., Modak, S., Acharjee, S., “Filter versus ideal on the topological spaces”, Advances in topology and their interdisciplinary applications, Springer, 183-195, (2023).
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Research Article
Yazarlar

Shyamapada Modak 0000-0002-0226-2392

Kulchhum Khatun Bu kişi benim 0000-0001-9202-6387

Jiarul Hoque 0000-0003-1055-9820

Erken Görünüm Tarihi 10 Kasım 2023
Yayımlanma Tarihi
Yayımlandığı Sayı Yıl 2025 Erken Görünüm

Kaynak Göster

APA Modak, S., Khatun, K., & Hoque, J. (2023). Characterizations of Filter Convergent in Terms of Ideal. Gazi University Journal of Science1-1. https://doi.org/10.35378/gujs.967261
AMA Modak S, Khatun K, Hoque J. Characterizations of Filter Convergent in Terms of Ideal. Gazi University Journal of Science. Published online 01 Kasım 2023:1-1. doi:10.35378/gujs.967261
Chicago Modak, Shyamapada, Kulchhum Khatun, ve Jiarul Hoque. “Characterizations of Filter Convergent in Terms of Ideal”. Gazi University Journal of Science, Kasım (Kasım 2023), 1-1. https://doi.org/10.35378/gujs.967261.
EndNote Modak S, Khatun K, Hoque J (01 Kasım 2023) Characterizations of Filter Convergent in Terms of Ideal. Gazi University Journal of Science 1–1.
IEEE S. Modak, K. Khatun, ve J. Hoque, “Characterizations of Filter Convergent in Terms of Ideal”, Gazi University Journal of Science, ss. 1–1, Kasım 2023, doi: 10.35378/gujs.967261.
ISNAD Modak, Shyamapada vd. “Characterizations of Filter Convergent in Terms of Ideal”. Gazi University Journal of Science. Kasım 2023. 1-1. https://doi.org/10.35378/gujs.967261.
JAMA Modak S, Khatun K, Hoque J. Characterizations of Filter Convergent in Terms of Ideal. Gazi University Journal of Science. 2023;:1–1.
MLA Modak, Shyamapada vd. “Characterizations of Filter Convergent in Terms of Ideal”. Gazi University Journal of Science, 2023, ss. 1-1, doi:10.35378/gujs.967261.
Vancouver Modak S, Khatun K, Hoque J. Characterizations of Filter Convergent in Terms of Ideal. Gazi University Journal of Science. 2023:1-.