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Role of ideals on $\sigma$-topological spaces

Year 2022, Volume: 71 Issue: 3, 870 - 883, 30.09.2022
https://doi.org/10.31801/cfsuasmas.1038097

Abstract

In this writeup, we have discussed the role of ideals on $\sigma$-topological spaces. Using this idea, we have also studied and discussed two operators $()^{*\sigma}$ and $\psi_{\sigma}$. We have extended this concept to a new generalized set and investigated some basic properties of these concepts using $()^{*\sigma}$ and $\psi_{\sigma}$ operators.

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References

  • Al-Omari, A., Noiri, T., On $\psi_*$-operator in ideal m-spaces, Bol. Soc. Paran. Mat., (3s.), 30(1) (2012), 53-66. https://doi.org/10.5269/bspm.v30i1.12787
  • Al-Omari, A., Noiri, T., Corrigendum to on $\psi_*$-operator in ideal m-spaces, Bol. Soc. Paran. Mat., (3s.), 30(2) (2012), 119-119. https://doi.org/10.5269/bspm.v30i2.14925
  • Al-Omari, A., Noiri, T., On operators in ideal minimal spaces, Mathematica, 58(81)(1-2) (2016), 3-13.
  • Al-Saadi, H., Al-Omari, A., Some operators in ideal topological spaces, Missouri J. Math. Sci., 30(1) (2018), 59-71. https://doi.org/ 10.35834/mjms/1534384955
  • Hamlett, T.R., Jankovi´c, D., Ideals in topological spaces and set operator $\psi$, Bull. U.M.I., 7(4-B) (1990), 863-874.
  • Jankovic, 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
  • Kuratowski, K., Topology, Vol. 1, Academic Press, New York, 1966.
  • Modak, S., Bandhyopadhyay, C., A note on $\psi$-operator, Bull. Malyas. Math. Sci. Soc., 30(1) (2007), 43-48.
  • Modak, S., Mistry, S., Ideal on supra topological space, Int. Journal of Math. Analysis, 6(1) (2012), 1-10.
  • Natkaniec, T., On I-continuity and I-semicontinuity points, Math. Slovaca, 36(3) (1986), 297- 312.
  • Newcomb, R.L., Topologies Which are Compact Codulo an Ideal, Ph.D. Dissertation, Univ. of Cal. at Santa Barbara, 1967.
  • Njastad, O., On some classes of nearly open sets, Pacific J. Math., 15(3) (1965), 961-970. https://doi.org/10.2140/pjm.1965.15.961
  • Vaidyanathaswamy, R., Set Topology, Chelsea Publishing Co., New York, 1960.
Year 2022, Volume: 71 Issue: 3, 870 - 883, 30.09.2022
https://doi.org/10.31801/cfsuasmas.1038097

Abstract

Project Number

NA

References

  • Al-Omari, A., Noiri, T., On $\psi_*$-operator in ideal m-spaces, Bol. Soc. Paran. Mat., (3s.), 30(1) (2012), 53-66. https://doi.org/10.5269/bspm.v30i1.12787
  • Al-Omari, A., Noiri, T., Corrigendum to on $\psi_*$-operator in ideal m-spaces, Bol. Soc. Paran. Mat., (3s.), 30(2) (2012), 119-119. https://doi.org/10.5269/bspm.v30i2.14925
  • Al-Omari, A., Noiri, T., On operators in ideal minimal spaces, Mathematica, 58(81)(1-2) (2016), 3-13.
  • Al-Saadi, H., Al-Omari, A., Some operators in ideal topological spaces, Missouri J. Math. Sci., 30(1) (2018), 59-71. https://doi.org/ 10.35834/mjms/1534384955
  • Hamlett, T.R., Jankovi´c, D., Ideals in topological spaces and set operator $\psi$, Bull. U.M.I., 7(4-B) (1990), 863-874.
  • Jankovic, 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
  • Kuratowski, K., Topology, Vol. 1, Academic Press, New York, 1966.
  • Modak, S., Bandhyopadhyay, C., A note on $\psi$-operator, Bull. Malyas. Math. Sci. Soc., 30(1) (2007), 43-48.
  • Modak, S., Mistry, S., Ideal on supra topological space, Int. Journal of Math. Analysis, 6(1) (2012), 1-10.
  • Natkaniec, T., On I-continuity and I-semicontinuity points, Math. Slovaca, 36(3) (1986), 297- 312.
  • Newcomb, R.L., Topologies Which are Compact Codulo an Ideal, Ph.D. Dissertation, Univ. of Cal. at Santa Barbara, 1967.
  • Njastad, O., On some classes of nearly open sets, Pacific J. Math., 15(3) (1965), 961-970. https://doi.org/10.2140/pjm.1965.15.961
  • Vaidyanathaswamy, R., Set Topology, Chelsea Publishing Co., New York, 1960.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences, Applied Mathematics
Journal Section Research Articles
Authors

Chhapikul Mıah 0000-0002-4965-1758

Md. Monirul Islam 0000-0003-4748-4690

Shyamapada Modak 0000-0002-0226-2392

Sukalyan Mistry 0000-0002-3308-5878

Project Number NA
Publication Date September 30, 2022
Submission Date December 19, 2021
Acceptance Date April 27, 2022
Published in Issue Year 2022 Volume: 71 Issue: 3

Cite

APA Mıah, C., Islam, M. M., Modak, S., Mistry, S. (2022). Role of ideals on $\sigma$-topological spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(3), 870-883. https://doi.org/10.31801/cfsuasmas.1038097
AMA Mıah C, Islam MM, Modak S, Mistry S. Role of ideals on $\sigma$-topological spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. September 2022;71(3):870-883. doi:10.31801/cfsuasmas.1038097
Chicago Mıah, Chhapikul, Md. Monirul Islam, Shyamapada Modak, and Sukalyan Mistry. “Role of Ideals on $\sigma$-Topological Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 3 (September 2022): 870-83. https://doi.org/10.31801/cfsuasmas.1038097.
EndNote Mıah C, Islam MM, Modak S, Mistry S (September 1, 2022) Role of ideals on $\sigma$-topological spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 3 870–883.
IEEE C. Mıah, M. M. Islam, S. Modak, and S. Mistry, “Role of ideals on $\sigma$-topological spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 3, pp. 870–883, 2022, doi: 10.31801/cfsuasmas.1038097.
ISNAD Mıah, Chhapikul et al. “Role of Ideals on $\sigma$-Topological Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/3 (September 2022), 870-883. https://doi.org/10.31801/cfsuasmas.1038097.
JAMA Mıah C, Islam MM, Modak S, Mistry S. Role of ideals on $\sigma$-topological spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:870–883.
MLA Mıah, Chhapikul et al. “Role of Ideals on $\sigma$-Topological Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 3, 2022, pp. 870-83, doi:10.31801/cfsuasmas.1038097.
Vancouver Mıah C, Islam MM, Modak S, Mistry S. Role of ideals on $\sigma$-topological spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(3):870-83.

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

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