Research Article
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Year 2025, Early View, 1 - 1

Shyamapada Modak Kulchhum Khatun Jiarul Hoque

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

Abstract

References

  • [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

Year 2025, Early View, 1 - 1

Shyamapada Modak Kulchhum Khatun Jiarul Hoque

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

Abstract

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.

Keywords

Net Filter Ultrafilter Ideal Local Function

References

  • [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).
There are 22 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Shyamapada Modak 0000-0002-0226-2392

Kulchhum Khatun This is me 0000-0001-9202-6387

Jiarul Hoque 0000-0003-1055-9820

Early Pub Date November 10, 2023
Publication Date
Published in Issue Year 2025 Early View

Cite

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 November 1, 2023:1-1. doi:10.35378/gujs.967261
Chicago Modak, Shyamapada, Kulchhum Khatun, and Jiarul Hoque. “Characterizations of Filter Convergent in Terms of Ideal”. Gazi University Journal of Science, November (November 2023), 1-1. https://doi.org/10.35378/gujs.967261.
EndNote Modak S, Khatun K, Hoque J (November 1, 2023) Characterizations of Filter Convergent in Terms of Ideal. Gazi University Journal of Science 1–1.
IEEE S. Modak, K. Khatun, and J. Hoque, “Characterizations of Filter Convergent in Terms of Ideal”, Gazi University Journal of Science, pp. 1–1, November 2023, doi: 10.35378/gujs.967261.
ISNAD Modak, Shyamapada et al. “Characterizations of Filter Convergent in Terms of Ideal”. Gazi University Journal of Science. November 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 et al. “Characterizations of Filter Convergent in Terms of Ideal”. Gazi University Journal of Science, 2023, pp. 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-.