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A stronger form of locally closed set and its homeomorphic image

Yıl 2024, Cilt: 73 Sayı: 1, 25 - 36, 16.03.2024

Jiarul Hoque Shyamapada Modak

https://doi.org/10.31801/cfsuasmas.1186168

Öz

Through this paper, via the operators $(\cdot)^{\star}$ and $\Psi$, we presented notion of $\star$-Locally set in an ideal topological space $\zeta_{\mathbb{I}}$ as a new stronger form of locally closed set, and considered relations with various existing weak form of locally closed set. Preservations of direct images as well as inverse images of $(\cdot)^{\star}$, $\Psi$, $\star$-perfect and various weak forms of locally closed set including $\star$-Locally closed set are important investigating part. Besides, we pointed out that consideration of `bijectivity' in Lemma 3.1 of [24] is sufficient, and the Lemma 3.3 of [24] is wrong. We demonstrated two modifications of the last one.

Anahtar Kelimeler

Ideal local function $\Psi$-operator locally closed set homeomorphism

Kaynakça

  • Al-Omari, A., Al-Saadi, H., A topology via $\omega$-local functions in ideal spaces, Mathematica, 60(83) (2018), 103–110. https://doi.org/10.24193/mathcluj.2018.2.01
  • Bandhopadhyay, C., Modak, S., A new topology via $\Psi$-operator, Proc. Nat. Acad. Sci. India, 76(A)(IV) (2006), 317–320.
  • Bourbaki, N., Elements of Mathematics, General Topology, Addison-Wesley, Reading, Massachusetts, 1966.
  • Bourbaki, N., General Topology, Chapter 1-4, Springer, 1989.
  • Choquet, G., Sur les notions de filter et grill, C.R. Acad. Sci. Paris, 224 (1947), 171—173.
  • Dontchev, J., Idealization of Ganster-Reilly decomposition theorems, arXIV:math.Gn/9901017v1 [math.GN], 1999. https://doi.org/10.48550/arXiv.math/9901017
  • Ganster, M., Reilly, I.L., Locally closed sets and LC-continuous functions, Int. J. Math. Math. Sci., 12(3) (1989), 417–424.
  • Hamlett, T.R., Jankovic, D., Ideals in topological spaces and the set operator $\Psi$, Boll. Uni. Mat. Ital., 7(4)(B) (1990), 863–874.
  • Hashimoto, H., On the $\star$-topology and its applications, Fund. Math., 91 (1976), 5–10.
  • Hayashi, E., Topologies defined by local properties, Math. Ann., 156 (1964), 205–215.
  • Jankovi´c, D., Hamlett, T.R., New topologies from old via ideals, Amer. Math. Monthly, 97 (1990), 295–310. https://doi.org/10.2307/2324512
  • Jeyanthi, V., Devi, V.R., Sivaraj, D., Subsets of ideal topological spaces, Acta Math. Hungar., 114 (2007), 117–131. https://doi.org/10.1007/s10474-006-0517-7
  • Kuratowski, K., Topology, Vol. I, Academic Press, New York, 1966.
  • Levine, N., Semi-open sets and semi continuity in topological spaces, Amer. Math. Monthly, 70(1) (1963), 36–41. https://doi.org/10.2307/2312781
  • Lugojan, S., Generalized topology, Stud. Cerc. Mat., 34 (1982), 348–360 .
  • Modak, S., Some new topologies on ideal topological spaces, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 82(3) (2012), 233–243. https://doi.org/10.1007/s40010-012-0039-3
  • Modak, S., Minimal spaces with a mathematical structure, J. Assoc. Arab Univ. Basic Appl. Sci., 22 (2017), 98–101. https://doi.org/10.1016/j.jaubas.2016.05.005
  • Modak, S., Bandyopadhyay, C., A note on ψ-operator, Bull. Malyas. Math. Sci. Soc., 30(1) (2007), 43–48.
  • Modak, S., Hoque, J., Selim, Sk., Homeomorphic image of some kernels, Cankaya Univ. J. Sci. Eng., 17(1) (2020), 52-62.
  • Modak, S., Noiri, T., Some generalizations of locally closed sets, Iran. J. Math. Sci. Inform., 14 (2019), 159–165. https://doi.org/10.7508/ijmsi.2019.01.014
  • Modak, S., Noiri, T., Remarks on locally closed set, Acta Comment. Univ. Tartu. Math., 22(1) (2018), 57–64. http://dx.doi.org/10.12697/ACUTM.2018.22.06
  • Natkaniec, T., On I-continuity and I-semicontinuity points, Math. Slovaca, 36(3) (1986), 297–312. http://dml.cz/dmlcz/128786
  • Samuel, P., A topology formed from a given topology and ideal, J. Lond. Math. Soc., 10 (1975), 409–416. https://doi.org/10.1112/jlms/s2-10.4.409
  • Selim, Sk., Noiri, T., Modak, S., Ideals and the associated filters on topological spaces, Euras. Bull. Math., 2(3) (2019), 80–85.
  • Stone, M.H., Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41 (1937), 375–481. https://doi.org/10.2307/1989788
  • Sundaram, P., Balachandran, K., Semi generalized locally closed sets in topological spaces, preprint.
  • Vaidyanathswamy, R., Set Topology, Chelsea Publishing Co., New York, 1960.

Yıl 2024, Cilt: 73 Sayı: 1, 25 - 36, 16.03.2024

Jiarul Hoque Shyamapada Modak

https://doi.org/10.31801/cfsuasmas.1186168

Öz

Kaynakça

  • Al-Omari, A., Al-Saadi, H., A topology via $\omega$-local functions in ideal spaces, Mathematica, 60(83) (2018), 103–110. https://doi.org/10.24193/mathcluj.2018.2.01
  • Bandhopadhyay, C., Modak, S., A new topology via $\Psi$-operator, Proc. Nat. Acad. Sci. India, 76(A)(IV) (2006), 317–320.
  • Bourbaki, N., Elements of Mathematics, General Topology, Addison-Wesley, Reading, Massachusetts, 1966.
  • Bourbaki, N., General Topology, Chapter 1-4, Springer, 1989.
  • Choquet, G., Sur les notions de filter et grill, C.R. Acad. Sci. Paris, 224 (1947), 171—173.
  • Dontchev, J., Idealization of Ganster-Reilly decomposition theorems, arXIV:math.Gn/9901017v1 [math.GN], 1999. https://doi.org/10.48550/arXiv.math/9901017
  • Ganster, M., Reilly, I.L., Locally closed sets and LC-continuous functions, Int. J. Math. Math. Sci., 12(3) (1989), 417–424.
  • Hamlett, T.R., Jankovic, D., Ideals in topological spaces and the set operator $\Psi$, Boll. Uni. Mat. Ital., 7(4)(B) (1990), 863–874.
  • Hashimoto, H., On the $\star$-topology and its applications, Fund. Math., 91 (1976), 5–10.
  • Hayashi, E., Topologies defined by local properties, Math. Ann., 156 (1964), 205–215.
  • Jankovi´c, D., Hamlett, T.R., New topologies from old via ideals, Amer. Math. Monthly, 97 (1990), 295–310. https://doi.org/10.2307/2324512
  • Jeyanthi, V., Devi, V.R., Sivaraj, D., Subsets of ideal topological spaces, Acta Math. Hungar., 114 (2007), 117–131. https://doi.org/10.1007/s10474-006-0517-7
  • Kuratowski, K., Topology, Vol. I, Academic Press, New York, 1966.
  • Levine, N., Semi-open sets and semi continuity in topological spaces, Amer. Math. Monthly, 70(1) (1963), 36–41. https://doi.org/10.2307/2312781
  • Lugojan, S., Generalized topology, Stud. Cerc. Mat., 34 (1982), 348–360 .
  • Modak, S., Some new topologies on ideal topological spaces, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 82(3) (2012), 233–243. https://doi.org/10.1007/s40010-012-0039-3
  • Modak, S., Minimal spaces with a mathematical structure, J. Assoc. Arab Univ. Basic Appl. Sci., 22 (2017), 98–101. https://doi.org/10.1016/j.jaubas.2016.05.005
  • Modak, S., Bandyopadhyay, C., A note on ψ-operator, Bull. Malyas. Math. Sci. Soc., 30(1) (2007), 43–48.
  • Modak, S., Hoque, J., Selim, Sk., Homeomorphic image of some kernels, Cankaya Univ. J. Sci. Eng., 17(1) (2020), 52-62.
  • Modak, S., Noiri, T., Some generalizations of locally closed sets, Iran. J. Math. Sci. Inform., 14 (2019), 159–165. https://doi.org/10.7508/ijmsi.2019.01.014
  • Modak, S., Noiri, T., Remarks on locally closed set, Acta Comment. Univ. Tartu. Math., 22(1) (2018), 57–64. http://dx.doi.org/10.12697/ACUTM.2018.22.06
  • Natkaniec, T., On I-continuity and I-semicontinuity points, Math. Slovaca, 36(3) (1986), 297–312. http://dml.cz/dmlcz/128786
  • Samuel, P., A topology formed from a given topology and ideal, J. Lond. Math. Soc., 10 (1975), 409–416. https://doi.org/10.1112/jlms/s2-10.4.409
  • Selim, Sk., Noiri, T., Modak, S., Ideals and the associated filters on topological spaces, Euras. Bull. Math., 2(3) (2019), 80–85.
  • Stone, M.H., Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41 (1937), 375–481. https://doi.org/10.2307/1989788
  • Sundaram, P., Balachandran, K., Semi generalized locally closed sets in topological spaces, preprint.
  • Vaidyanathswamy, R., Set Topology, Chelsea Publishing Co., New York, 1960.
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Jiarul Hoque 0000-0003-1055-9820

Shyamapada Modak 0000-0002-0226-2392

Yayımlanma Tarihi 16 Mart 2024
Gönderilme Tarihi 8 Ekim 2022
Kabul Tarihi 30 Eylül 2023
Yayımlandığı Sayı Yıl 2024 Cilt: 73 Sayı: 1

Kaynak Göster

APA Hoque, J., & Modak, S. (2024). A stronger form of locally closed set and its homeomorphic image. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(1), 25-36. https://doi.org/10.31801/cfsuasmas.1186168
AMA Hoque J, Modak S. A stronger form of locally closed set and its homeomorphic image. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Mart 2024;73(1):25-36. doi:10.31801/cfsuasmas.1186168
Chicago Hoque, Jiarul, ve Shyamapada Modak. “A Stronger Form of Locally Closed Set and Its Homeomorphic Image”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, sy. 1 (Mart 2024): 25-36. https://doi.org/10.31801/cfsuasmas.1186168.
EndNote Hoque J, Modak S (01 Mart 2024) A stronger form of locally closed set and its homeomorphic image. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 1 25–36.
IEEE J. Hoque ve S. Modak, “A stronger form of locally closed set and its homeomorphic image”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 73, sy. 1, ss. 25–36, 2024, doi: 10.31801/cfsuasmas.1186168.
ISNAD Hoque, Jiarul - Modak, Shyamapada. “A Stronger Form of Locally Closed Set and Its Homeomorphic Image”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/1 (Mart 2024), 25-36. https://doi.org/10.31801/cfsuasmas.1186168.
JAMA Hoque J, Modak S. A stronger form of locally closed set and its homeomorphic image. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73:25–36.
MLA Hoque, Jiarul ve Shyamapada Modak. “A Stronger Form of Locally Closed Set and Its Homeomorphic Image”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 73, sy. 1, 2024, ss. 25-36, doi:10.31801/cfsuasmas.1186168.
Vancouver Hoque J, Modak S. A stronger form of locally closed set and its homeomorphic image. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73(1):25-36.

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

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