Research Article
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Year 2025, Volume: 74 Issue: 2, 180 - 190, 19.06.2025
https://doi.org/10.31801/cfsuasmas.1476888

Abstract

References

  • Abd El-Monsef, M. E., El-Deeb, S. N., Mahmoud, R. A., β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12 (1983), 77–90.
  • Acharjee, S., Özkoç, M., Issaka, F. Y., Primal Topological Spaces, Bol. Soc. Paran. Mat., 43 (2025), 1–9. https://doi.org/10.5269/bspm.66792.
  • Alghamdi, O., Al-Omari, A., Alqahtani, M. H., Novel operators in the frame of primal topological spaces, AIMS Mathematics, 9(9) (2024), 25792–25808. https://doi.org/10.3934/math.20241260.
  • Al-Omari, A., Acharjee, S., Özkoç, M., A new operator of primal topological spaces, Mathematica, 65(88)(2) (2023), 175–183. https://doi.org/10.24193/mathcluj.2023.2.03.
  • Al-Omari, A., Özkoç, M., Acharjee, S., Primal-proximity spaces, Mathematica, 66(89)(2) (2024), 151–167. https://doi.org/10.24193/mathcluj.2024.2.01.
  • Al-Omari, A., Alghami, O., Regularity and normality on primal spaces, AIMS Mathematics, 9 (2024), 7662–7672. https://doi.org/10.3934/math.2024372.
  • Al-Omari, A., Alqahtani, M. H., Primal structure with closure operators and their applications, Mathematics, 11(24) (2023), 4946. https://doi.org/10.3390/math11244946.
  • Al-Omari, A., Alqahtani, M. H., Some operators in soft primal spaces, AIMS Mathematics, 96(5) (2024), 10756–10774. https://doi.org/10.3934/math.2024525.
  • Al-Saadi, H., Al-Hodieb, M., Sets Related to Openness and Continuity Decompositions in Primal Topological Spaces, Eur. j. pure appl., 17(2) (2024), 1352–1368. https://doi.org/10.29020/nybg.ejpam.v17i2.5171.
  • Al-Saadi, H., Al-Malki, H., Categories of open sets in generalized primal topological spaces, Mathematics, 12 (2024), 207. https://doi.org/10.3390/math12020207.
  • Al-Saadi, H., Al-Malki, H., Generalized primal topological spaces, AIMS Mathematics, 8(10) (2023), 24162–24175. https://doi.org/10.3934/math.20231232.
  • Al-Shami, T. M., Ameen, Z. A., Gdairi, R. A., Mhemdi, A., On primal soft topology, Mathematics, 11(10) (2023), 2329. https://doi.org/10.3390/math11102329.
  • Chattopadhyay, C., Bandyopadhyay, C., On structure of δ-sets, Bull. Cal. Math. Soc., 83 (1991), 281–290. https://doi.org/10.1007/s10474-006-0520-z.
  • Hayashi, E., Topologies defined by local properties, Math. Ann., 156 (1964), 205–215. https://doi.org/10.1007/BF01363287.
  • Janković, D., Hamlett, T. R., New topologies from old via ideals, Amer. Math. Monthly, 97 (1990), 295–300. https://doi.org/10.1080/00029890.1990.11995593.
  • Kostyrko, P., Šalát, T., Wilczy\'{n}ski, W., $\mathcal{I}-$−convergence, Real Anal. Exchange, 26(2) (2000-2001), 669-785.
  • Kuratowski, K., Topology, Vol.1, Academic Press, New York, 1966.
  • Levine, N., Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36–41. https://doi.org/10.1080/00029890.1963.11990039.
  • Mashhour, A. S., Abd El-monsef, M. E., El-Deeb, N., On precontinuous and weak precontinuous mappings, Proc. Math. and Phy. Soc. Egypt, 53 (1982), 47–53.
  • Matejdes, M., On Topologies Induced by Ideals, Primals, Filters and Grills, Axioms, 13(10), 698 (2024), 1–16. https://doi.org/10.3390/axioms13100698.
  • Modak, S., Topology of grill filter space and continuity, Bol. Soc. Paran. Mat., 31(2) (2013), 219–230. https://doi.org/10.5269/bspm.v31i2.16603.
  • Modak, S., Grill-filter space, J. Indian Math. Soc., 80(3-4) (2013), 313–320.
  • Modak, S., Selim, S., Set operators and associated functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 70(1) (2021), 456–467. https://doi.org/10.31801/cfsuasmas.644689.
  • Natkaniec T., On I-continuity and I-semi continuity points, Math Slovaca, 36(3) (1986), 297–312. http://dml.cz/dmlcz/128786.
  • Njåstad O., On some classes of nearly open sets, Pacific J. Math, 15 (1965), 961–970. https://doi.org/10.2140/pjm.1965.15.961.
  • Özkoç, M., Köstel, B., On the topology $\tau^{\diamond}_{R}$ of primal topological spaces, AIMS Mathematics, 9(7) (2024), 17171-17183. https://doi.org/10.3934/math.2024834.
  • Şaşmaz, P., Özkoç, M., On a new operator based on a primal and its associated topology, Eur. J. Pure Appl. Math., 17(4) (2024), 2800-2811. https://doi.org/10.29020/nybg.ejpam.v17i4.5369.
  • Stone, M. H., Application of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41 (1937), 375–481. https://doi.org/10.1090/S0002-9947-1937-1501905-7.
  • Vaidyanathswamy R., Set topology, Chelsea Publishing Company, New York, 1960.
  • Willard, S., General Topology, Addison-Wesley Publishing Company, USA, 1970.

Variants of sets and functions with primals

Year 2025, Volume: 74 Issue: 2, 180 - 190, 19.06.2025
https://doi.org/10.31801/cfsuasmas.1476888

Abstract

Through this paper, we will discuss the limit points of a set and its complement set. To do this the authors will consider Acherjee et al.’s mathematical structure primal. These limit points via primal will further express the representation of nowhere dense sets in the literature. Expression of ⋄-local function and its associated set-valued set function will also be discussed here. Levine’s semi-open sets will also be further represented by these limit points and will be decomposed.

References

  • Abd El-Monsef, M. E., El-Deeb, S. N., Mahmoud, R. A., β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12 (1983), 77–90.
  • Acharjee, S., Özkoç, M., Issaka, F. Y., Primal Topological Spaces, Bol. Soc. Paran. Mat., 43 (2025), 1–9. https://doi.org/10.5269/bspm.66792.
  • Alghamdi, O., Al-Omari, A., Alqahtani, M. H., Novel operators in the frame of primal topological spaces, AIMS Mathematics, 9(9) (2024), 25792–25808. https://doi.org/10.3934/math.20241260.
  • Al-Omari, A., Acharjee, S., Özkoç, M., A new operator of primal topological spaces, Mathematica, 65(88)(2) (2023), 175–183. https://doi.org/10.24193/mathcluj.2023.2.03.
  • Al-Omari, A., Özkoç, M., Acharjee, S., Primal-proximity spaces, Mathematica, 66(89)(2) (2024), 151–167. https://doi.org/10.24193/mathcluj.2024.2.01.
  • Al-Omari, A., Alghami, O., Regularity and normality on primal spaces, AIMS Mathematics, 9 (2024), 7662–7672. https://doi.org/10.3934/math.2024372.
  • Al-Omari, A., Alqahtani, M. H., Primal structure with closure operators and their applications, Mathematics, 11(24) (2023), 4946. https://doi.org/10.3390/math11244946.
  • Al-Omari, A., Alqahtani, M. H., Some operators in soft primal spaces, AIMS Mathematics, 96(5) (2024), 10756–10774. https://doi.org/10.3934/math.2024525.
  • Al-Saadi, H., Al-Hodieb, M., Sets Related to Openness and Continuity Decompositions in Primal Topological Spaces, Eur. j. pure appl., 17(2) (2024), 1352–1368. https://doi.org/10.29020/nybg.ejpam.v17i2.5171.
  • Al-Saadi, H., Al-Malki, H., Categories of open sets in generalized primal topological spaces, Mathematics, 12 (2024), 207. https://doi.org/10.3390/math12020207.
  • Al-Saadi, H., Al-Malki, H., Generalized primal topological spaces, AIMS Mathematics, 8(10) (2023), 24162–24175. https://doi.org/10.3934/math.20231232.
  • Al-Shami, T. M., Ameen, Z. A., Gdairi, R. A., Mhemdi, A., On primal soft topology, Mathematics, 11(10) (2023), 2329. https://doi.org/10.3390/math11102329.
  • Chattopadhyay, C., Bandyopadhyay, C., On structure of δ-sets, Bull. Cal. Math. Soc., 83 (1991), 281–290. https://doi.org/10.1007/s10474-006-0520-z.
  • Hayashi, E., Topologies defined by local properties, Math. Ann., 156 (1964), 205–215. https://doi.org/10.1007/BF01363287.
  • Janković, D., Hamlett, T. R., New topologies from old via ideals, Amer. Math. Monthly, 97 (1990), 295–300. https://doi.org/10.1080/00029890.1990.11995593.
  • Kostyrko, P., Šalát, T., Wilczy\'{n}ski, W., $\mathcal{I}-$−convergence, Real Anal. Exchange, 26(2) (2000-2001), 669-785.
  • Kuratowski, K., Topology, Vol.1, Academic Press, New York, 1966.
  • Levine, N., Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36–41. https://doi.org/10.1080/00029890.1963.11990039.
  • Mashhour, A. S., Abd El-monsef, M. E., El-Deeb, N., On precontinuous and weak precontinuous mappings, Proc. Math. and Phy. Soc. Egypt, 53 (1982), 47–53.
  • Matejdes, M., On Topologies Induced by Ideals, Primals, Filters and Grills, Axioms, 13(10), 698 (2024), 1–16. https://doi.org/10.3390/axioms13100698.
  • Modak, S., Topology of grill filter space and continuity, Bol. Soc. Paran. Mat., 31(2) (2013), 219–230. https://doi.org/10.5269/bspm.v31i2.16603.
  • Modak, S., Grill-filter space, J. Indian Math. Soc., 80(3-4) (2013), 313–320.
  • Modak, S., Selim, S., Set operators and associated functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 70(1) (2021), 456–467. https://doi.org/10.31801/cfsuasmas.644689.
  • Natkaniec T., On I-continuity and I-semi continuity points, Math Slovaca, 36(3) (1986), 297–312. http://dml.cz/dmlcz/128786.
  • Njåstad O., On some classes of nearly open sets, Pacific J. Math, 15 (1965), 961–970. https://doi.org/10.2140/pjm.1965.15.961.
  • Özkoç, M., Köstel, B., On the topology $\tau^{\diamond}_{R}$ of primal topological spaces, AIMS Mathematics, 9(7) (2024), 17171-17183. https://doi.org/10.3934/math.2024834.
  • Şaşmaz, P., Özkoç, M., On a new operator based on a primal and its associated topology, Eur. J. Pure Appl. Math., 17(4) (2024), 2800-2811. https://doi.org/10.29020/nybg.ejpam.v17i4.5369.
  • Stone, M. H., Application of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41 (1937), 375–481. https://doi.org/10.1090/S0002-9947-1937-1501905-7.
  • Vaidyanathswamy R., Set topology, Chelsea Publishing Company, New York, 1960.
  • Willard, S., General Topology, Addison-Wesley Publishing Company, USA, 1970.
There are 30 citations in total.

Details

Primary Language English
Subjects Topology
Journal Section Research Articles
Authors

Chhapikul Mıah 0000-0002-4965-1758

Monoj Kumar Das 0009-0007-2107-9984

Shyamapada Modak 0000-0002-0226-2392

Publication Date June 19, 2025
Submission Date May 1, 2024
Acceptance Date February 17, 2025
Published in Issue Year 2025 Volume: 74 Issue: 2

Cite

APA Mıah, C., Das, M. K., & Modak, S. (2025). Variants of sets and functions with primals. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 74(2), 180-190. https://doi.org/10.31801/cfsuasmas.1476888
AMA Mıah C, Das MK, Modak S. Variants of sets and functions with primals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2025;74(2):180-190. doi:10.31801/cfsuasmas.1476888
Chicago Mıah, Chhapikul, Monoj Kumar Das, and Shyamapada Modak. “Variants of Sets and Functions With Primals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74, no. 2 (June 2025): 180-90. https://doi.org/10.31801/cfsuasmas.1476888.
EndNote Mıah C, Das MK, Modak S (June 1, 2025) Variants of sets and functions with primals. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74 2 180–190.
IEEE C. Mıah, M. K. Das, and S. Modak, “Variants of sets and functions with primals”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 74, no. 2, pp. 180–190, 2025, doi: 10.31801/cfsuasmas.1476888.
ISNAD Mıah, Chhapikul et al. “Variants of Sets and Functions With Primals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74/2 (June2025), 180-190. https://doi.org/10.31801/cfsuasmas.1476888.
JAMA Mıah C, Das MK, Modak S. Variants of sets and functions with primals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025;74:180–190.
MLA Mıah, Chhapikul et al. “Variants of Sets and Functions With Primals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 74, no. 2, 2025, pp. 180-9, doi:10.31801/cfsuasmas.1476888.
Vancouver Mıah C, Das MK, Modak S. Variants of sets and functions with primals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025;74(2):180-9.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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