i-Semi-Inter-Open Sets in Topological Spaces

i-Semi-Inter Open Sets In Topological Spaces

Section: Research Article
Issue
Vol. 35 No. 2 (2026): Volume 35, Issue 2
Pages
1-14

Keywords:

i ــ οpen sets, iــsemi ــinter-οpen sets, iــsemi-interــ closed sets, Semiــ οpen sets, Semiــinter οpen sets

Abstract

This work introduces a novel class of  sets are called -semi-inter open sets and semi-inter open sets in topological spaces.


A number of mathematical arguments have been used to thoroughly examine some of these sets' characteristics and their connections to other kinds of sets, including, for example we proved that in any topological space   : Each  is semi inter open set and semi-inter open set, each set is semi-inter open set and semi inter open set, each semi inter open set is -open set and semi inter open set, each open set is semi inter open set and semi inter open set, however, generally speaking the converses are not necessary to be valid. Also, we defined the topologically extended and non-topologically extended property for -semi-inter sets, and we show that the family of -semi inter open sets is not necessarily a topological space, with some characterizations as -semi-inter limit points, -semi-inter boundary of a set.

References

  1. M.E. Abd El Monsef, S.N. El-Deeb and R.A. Mahmoud, “β-open sets and β-continuity mapping”, Bull. Fac. Sci. Assuit. Univ., Vol. 12, No.1, pp. 1-18, (1983).
  2. S. W. Askandar, “On i-Separation Axioms”, International Journalof Scientific and Engineering Research, Vol. 7, No. 5, pp. 367-373 ,(2016).
  3. G. S. Ashaea and Y. Y. Yousif, “Some Types of Mappings in Bitopological Spaces”, Baghdad Science Journal, Vol. 18, No.1, pp.149-155, 2021. DOI:http://dx.doi.org/10.21123/bsj.2020.18.1.0149
  4. D.E. Cameron, “properties of S-closed spaces”, proc. Amer. Math. Soc., Vol. 72, No.3, pp. 581-586, (1978).
  5. A., Dimitrije “On b-open sets”, Math. Bech. Vol.48, pp.59-64, (1996).
  6. N. Levine, “Semi-open sets and semi-continuity in topological space”, Amer. Math. Monthly, Vol. 70, pp. 36-41, (1963). https://doi.org/10.1080/00029890.1963.11990039
  7. A.S. Mashhour, M.E. Abd El Monsef and S.N. El-Deeb, “On precontinuous and weak precontinuous Mappings”, Mathematical Physical and Engineering Sciences, Vol. 53, pp. 47-53,(1982). https://cir.nii.ac.jp/crid/1573950400472990592
  8. A.A. Mohammed and B.S. Abdullah, “ii-Open sets in topological spaces”. International Mathematics Forum, Vol. 14, No.1, pp. 41-48, (2019),. DOI: https://doi.org/10.12988/imf.2019.913
  9. O. Njastad, “On some classes of nearly open sets”, pacific J. Math. Vol. 15, pp. 961-970, (1965).
  10. DOI: 10.2140/pjm.1965.15.961
  11. T. Ohba and J. A. Umehara, “A simple proof of τ^α being a topology”, Mem.Fac.Sci.Kochi Univ. Ser. A Math, Vol. 21, pp. 87-88, (2000). https://cir.nii.ac.jp/crid/1570009750799037440
  12. W. Pervin, “Foundation of General Topology, translated by Attallah Thamir Al-Ani”, Mosul Univ,(1985).
  13. W. Pervin, “Foundation of General Topology”, Academic press, (1964).
  14. E.A. Saleh and B.M. Sulaiman, “Micro topological space with grill-generalized open sets”, Journal of Interdisciplinary, Vol. 26, No.7,pp .1439-1447, (2023). doi/10.47974/JIM-1562
  15. M.K. Singal and A.R. Singal, “Almost continuity mapping”, Yokohama Math. J., Vol. 16, pp. 63-73, (1968).
  16. N.V. Velicko, “H closed topological spaces”, Amer. Math. Soc. Transl., Vol. 78, No. 2, pp. 103-118, (1967). https://cir.nii.ac.jp/crid/1572543024587207808
  17. Y. Y. Yousif and N. A. Hussein, “α–connected fibrewise topological spaces”, Journal of Interdisciplinary Mathematics, Vol. 27, No. 4, pp. 827–834, (2024). https://doi.org/10.47974/JIM-1878.

Authors

Balsam Jarjees

Department of Mathematics, Collage of Education for Pure Science, Mosul University, Mosul, Iraq

Sabih Askandar

university of mosul/college of education for pure sciences/mathematics department

Identifiers

DOI: 10.33899/jes.v35i2.53681

Download this PDF file
PDF

Statistics

How to Cite

[1]
“i-Semi-Inter-Open Sets in Topological Spaces: i-Semi-Inter Open Sets In Topological Spaces”, JES, vol. 35, no. 2, pp. 1–14, Apr. 2026, doi: 10.33899/jes.v35i2.53681.
Copyright and Licensing
Creative Commons License

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

How to Cite

[1]
“i-Semi-Inter-Open Sets in Topological Spaces: i-Semi-Inter Open Sets In Topological Spaces”, JES, vol. 35, no. 2, pp. 1–14, Apr. 2026, doi: 10.33899/jes.v35i2.53681.