Year 2025,
Volume: 74 Issue: 2, 180 - 190, 19.06.2025
Chhapikul Mıah
,
Monoj Kumar Das
,
Shyamapada Modak
References
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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.
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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.
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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.
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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.
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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.
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Al-Omari, A., Alghami, O., Regularity and normality on primal spaces, AIMS Mathematics, 9 (2024), 7662–7672. https://doi.org/10.3934/math.2024372.
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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.
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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.
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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.
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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.
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Al-Saadi, H., Al-Malki, H., Generalized primal topological spaces, AIMS Mathematics, 8(10) (2023), 24162–24175.
https://doi.org/10.3934/math.20231232.
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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.
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https://doi.org/10.1007/s10474-006-0520-z.
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Hayashi, E., Topologies defined by local properties, Math. Ann., 156 (1964), 205–215. https://doi.org/10.1007/BF01363287.
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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.
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Kostyrko, P., Šalát, T., Wilczy\'{n}ski, W., $\mathcal{I}-$−convergence, Real Anal. Exchange, 26(2) (2000-2001), 669-785.
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Math. and Phy. Soc. Egypt, 53 (1982), 47–53.
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Matejdes, M., On Topologies Induced by Ideals, Primals, Filters and Grills, Axioms, 13(10), 698 (2024), 1–16.
https://doi.org/10.3390/axioms13100698.
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Modak, S., Grill-filter space, J. Indian Math. Soc., 80(3-4) (2013), 313–320.
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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.
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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.
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Vaidyanathswamy R., Set topology, Chelsea Publishing Company, New York, 1960.
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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
Chhapikul Mıah
,
Monoj Kumar Das
,
Shyamapada Modak
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.