Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2021, Cilt: 70 Sayı: 1, 456 - 467, 30.06.2021

Shyamapada Modak Sk Selim

https://doi.org/10.31801/cfsuasmas.644689
Cited By: 2

Öz

Kaynakça

  • Al-Omari, A., Modak, S. and Noiri T., On θ-modifications of generalized topologies via hereditary classes, Commun. Korean Math. Soc. 31(4) (2016), 857-868. https://doi.org/10.4134/CKMS.c160002
  • Bandhopadhya, C. and Modak, S., A new topology via Ψ-operator, Proc. Nat. Acad. Sci. India, Sect. A Phys. Sci. 76(A)(IV) (2006), 317-320.
  • Dontchev, J., Idealization of Ganster-Reilly decomposition theorems, arXIV:math. Gn/9901017v1 [math.GN], 5 Jan 1999.
  • Dontchev, J., Ganster, M. and Rose, D., Ideal resolvability, Topology Appl. 93 (1999), 1-16. https://doi.org/10.1016/S0166-8641(97)00257-5
  • Hamlett, T. R. and Jankovic, D., Ideals in topological spaces and the set operator, Boll. Un. Mat.Ital. 4-B(7) (1990), 863-874.
  • Hashimoto, H., On the *-topology and its applications, Fund. Math. 91 (1976), 5-10.
  • Hayashi, E., Topologies defined by local properties, Math. Ann. 156 (1964), 205-215.
  • Jankovic, D. and Hamlett, T. R., New topologies from old via ideals, Amer. Math. Monthly 97 (1990), 295-310, https://doi.org/10.1080/00029890.1990.11995593.
  • Kuratowski, K., Topology, Vol. I, New York, Academic Press, 1966.
  • 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/s40010-0120039-3
  • Modak, S., Operators on grill M-space, Bol. Soc. Paran. Mat. 31(2) (2013), 101-107. https://doi.org/10.5269/bspm.v31i2.15547
  • Modak, S., Grill-filter spacs, J.Indian Math. Soc. 80(3-4) (2013), 313-320.
  • 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. and Bandyopadhyay, C., A note on Ψ-operator, Bull. Malays. Math. Sci. Soc. 30(1) (2007), 43-48.
  • Modak, S., Garai, B. Mistry, S., Remarks on ideal M-space, Ann. Univ. Oradea Fasc. Mat. 19(1) (2012), 207-215.
  • Modak, S. and Noiri, T., Connectedness of ideal topological spaces, Filomat 29(4) (2015), 661-665.https://doi.org/10.2298/FIL1504661M
  • Newcomb, R. L., Topologies which are compact modulo an ideal, Ph. D. Dissertation, Univ. of Cal. at Santa Barbara (1967).
  • Natkaniec, T., On I-continuity and I-semicontinuity points, Math. Slovaca 36(3) (1986), 297-312.
  • Samuel, P., A topology formed from a given topology and ideal, J. London Math. Soc. 10 (1975), 409-416.
  • Selim, Sk., Islam., Md. M. and Modak, S., Characterizations of Hayashi-Samuel Spaces via Boundary Points, Commun. Adv. Math. Sci. 2(3) (2019), 219-226. https://doi.org/10.33434/cams.546925
  • Vaidyanathswamy, R., The localization theory in set-topology, Proc. Indian Acad. Sci. 20 (1945), 51-61. https://doi.org/10.1007/BF03048958

Set operators and associated functions

Yıl 2021, Cilt: 70 Sayı: 1, 456 - 467, 30.06.2021

Shyamapada Modak Sk Selim

https://doi.org/10.31801/cfsuasmas.644689
Cited By: 2

Öz

The study of two operators local function and the set operator $\psi$ on the ideal topological spaces are likely to be same to the study of closure and interior operator of the topological spaces. However, they are not exactly equal with the interior and closure operator of the topological spaces. In this context, we introduce two new set operators on the ideal topological spaces. Detail properties of these two operators are the part of this article. Furthermore, the operators interior (resp. $\psi$) and closure (local function) obey the relation $Int(A)$= X \ $Cl$(X \ A) (resp. $\psi$(A) = X \(X \A)$^*)$. We search the general method of these relations, through this manuscript.

Anahtar Kelimeler

local function associated function $\psi_M$ operator $\psi$ operator

Kaynakça

  • Al-Omari, A., Modak, S. and Noiri T., On θ-modifications of generalized topologies via hereditary classes, Commun. Korean Math. Soc. 31(4) (2016), 857-868. https://doi.org/10.4134/CKMS.c160002
  • Bandhopadhya, C. and Modak, S., A new topology via Ψ-operator, Proc. Nat. Acad. Sci. India, Sect. A Phys. Sci. 76(A)(IV) (2006), 317-320.
  • Dontchev, J., Idealization of Ganster-Reilly decomposition theorems, arXIV:math. Gn/9901017v1 [math.GN], 5 Jan 1999.
  • Dontchev, J., Ganster, M. and Rose, D., Ideal resolvability, Topology Appl. 93 (1999), 1-16. https://doi.org/10.1016/S0166-8641(97)00257-5
  • Hamlett, T. R. and Jankovic, D., Ideals in topological spaces and the set operator, Boll. Un. Mat.Ital. 4-B(7) (1990), 863-874.
  • Hashimoto, H., On the *-topology and its applications, Fund. Math. 91 (1976), 5-10.
  • Hayashi, E., Topologies defined by local properties, Math. Ann. 156 (1964), 205-215.
  • Jankovic, D. and Hamlett, T. R., New topologies from old via ideals, Amer. Math. Monthly 97 (1990), 295-310, https://doi.org/10.1080/00029890.1990.11995593.
  • Kuratowski, K., Topology, Vol. I, New York, Academic Press, 1966.
  • 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/s40010-0120039-3
  • Modak, S., Operators on grill M-space, Bol. Soc. Paran. Mat. 31(2) (2013), 101-107. https://doi.org/10.5269/bspm.v31i2.15547
  • Modak, S., Grill-filter spacs, J.Indian Math. Soc. 80(3-4) (2013), 313-320.
  • 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. and Bandyopadhyay, C., A note on Ψ-operator, Bull. Malays. Math. Sci. Soc. 30(1) (2007), 43-48.
  • Modak, S., Garai, B. Mistry, S., Remarks on ideal M-space, Ann. Univ. Oradea Fasc. Mat. 19(1) (2012), 207-215.
  • Modak, S. and Noiri, T., Connectedness of ideal topological spaces, Filomat 29(4) (2015), 661-665.https://doi.org/10.2298/FIL1504661M
  • Newcomb, R. L., Topologies which are compact modulo an ideal, Ph. D. Dissertation, Univ. of Cal. at Santa Barbara (1967).
  • Natkaniec, T., On I-continuity and I-semicontinuity points, Math. Slovaca 36(3) (1986), 297-312.
  • Samuel, P., A topology formed from a given topology and ideal, J. London Math. Soc. 10 (1975), 409-416.
  • Selim, Sk., Islam., Md. M. and Modak, S., Characterizations of Hayashi-Samuel Spaces via Boundary Points, Commun. Adv. Math. Sci. 2(3) (2019), 219-226. https://doi.org/10.33434/cams.546925
  • Vaidyanathswamy, R., The localization theory in set-topology, Proc. Indian Acad. Sci. 20 (1945), 51-61. https://doi.org/10.1007/BF03048958
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Shyamapada Modak 0000-0002-0226-2392

Sk Selim Bu kişi benim 0000-0002-4226-2004

Yayımlanma Tarihi 30 Haziran 2021
Gönderilme Tarihi 9 Kasım 2019
Kabul Tarihi 3 Mart 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 70 Sayı: 1

Kaynak Göster

APA Modak, S., & Selim, S. (2021). Set operators and associated functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(1), 456-467. https://doi.org/10.31801/cfsuasmas.644689
AMA Modak S, Selim S. Set operators and associated functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2021;70(1):456-467. doi:10.31801/cfsuasmas.644689
Chicago Modak, Shyamapada, ve Sk Selim. “Set Operators and Associated Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, sy. 1 (Haziran 2021): 456-67. https://doi.org/10.31801/cfsuasmas.644689.
EndNote Modak S, Selim S (01 Haziran 2021) Set operators and associated functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 456–467.
IEEE S. Modak ve S. Selim, “Set operators and associated functions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 70, sy. 1, ss. 456–467, 2021, doi: 10.31801/cfsuasmas.644689.
ISNAD Modak, Shyamapada - Selim, Sk. “Set Operators and Associated Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (Haziran 2021), 456-467. https://doi.org/10.31801/cfsuasmas.644689.
JAMA Modak S, Selim S. Set operators and associated functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:456–467.
MLA Modak, Shyamapada ve Sk Selim. “Set Operators and Associated Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 70, sy. 1, 2021, ss. 456-67, doi:10.31801/cfsuasmas.644689.
Vancouver Modak S, Selim S. Set operators and associated functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):456-67.

Cited By

Characterization of Two Specific Cases with New Operators in Ideal Topological Spaces
Journal of New Theory
https://doi.org/10.53570/jnt.1418949
New types of connectedness and intermediate value theorem in ideal topological spaces
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
https://doi.org/10.31801/cfsuasmas.1075157

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

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.