Siboid Topological Spaces

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-24-2026-29
Published: Jan 29, 2026
Cite as:
Santanu Acharjee, Upashana Gogoi, Kyriakos Papadopoulos, Siboid Topological Spaces, Int. J. Anal. Appl., 24 (2026), 29.

Main Article Content

Santanu Acharjee, Upashana Gogoi, Kyriakos Papadopoulos

Abstract

In this article we introduce a new notion in topology that we call ‘siboid’, which yields to siboid topological spaces. We prove several fundamental results regarding siboid topological spaces. We define two new operators (.)∗ and Φ and a new map clθ that satisfies the Kuratowski closure axioms whenever the siboid satisfies the property R. Moreover, various types of generalized open sets and generalized continuous functions are defined and studied, and ‘siboid’ is then connected with Boolean algebra.

Article Details

References

  1. H. Cartan, Th'{e}orie des Filtres, C. R. Math. Acad. Sci. Paris 205 (1937), 595–598.
  2. K. Kuratowski, Topology, Volume I, Academic Press, 1966.
  3. G. Ch'{o}quet, Sur les Notions de Filter et Grille, C. R. Math. Acad. Sci. Paris 224 (1947), 171–173.
  4. S. Acharjee, M. Ozkoc, F.Y. Issaka, Primal Topological Spaces, Bol. Soc. Parana. Mat. 43 (2025), 1–9. https://doi.org/10.5269/bspm.66792.
  5. A. Al-Omari, S. Acharjee, M. Özkoc, A New Operator of Primal Topological Spaces, Mathematica 65 (88) (2023), 175–183. https://doi.org/10.24193/mathcluj.2023.2.03.
  6. D. Janković, T.R. Hamlett, New Topologies from Old via Ideals, Am. Math. Mon. 97 (1990), 295–310. https://doi.org/10.1080/00029890.1990.11995593.
  7. R. Manoharan, P. Thangavelu, Some New Sets and Topologies in Ideal Topological Spaces, Chin. J. Math. 2013 (2013), 973608. https://doi.org/10.1155/2013/973608.
  8. B. Roy, M. N. Mukherjee, On a Typical Topology Induced by a Grill, Soochow J. Math. 33 (2007), 771–786.
  9. A. Al-Omari and T. Noiri, Local Closure Functions in Ideal Topological Spaces, Novi Sad J. Math. 43 (2013), 139–149.
  10. E. Ekici and T. Noiri, Connectedness in Ideal Topological Spaces, Novi Sad J. Math 38 (2008), 65–70.
  11. S. Modak, Topology on Grill-Filter Space and Continuity, Bol. Soc. Paran. Mat. 31 (2013), 219–230. https://doi.org/10.5269/bspm.v31i2.16603.
  12. A. Al-Omari, M. Özkoc, S. Acharjee, Primal-Proximity Spaces, Mathematica 66 (2024), 151–167. https://doi.org/10.24193/mathcluj.2024.2.01.
  13. H. Al-Saadi, H. Al-Malki, Categories of Open Sets in Generalized Primal Topological Spaces, Mathematics 12 (2024), 207. https://doi.org/10.3390/math12020207.
  14. A. Al-Omari, O. Alghamdi, Regularity and Normality on Primal Spaces, AIMS Math. 9 (2024), 7662–7672. https://doi.org/10.3934/math.2024372.
  15. T.R. Hamlett, Ideals in Topological Spaces and the Set Operator $Psi$, Boll. Un. Mat. Ital. 7 (1990), 863–874.
  16. A. Al-Omari, T. Noiri, On ${tilde{Psi}}_{mathcal{G}}$-Sets in Grill Topological Spaces, Filomat 25 (2011), 187–196. https://doi.org/10.2298/FIL1102187A.
  17. A. Al-Omari, T. Noiri, On $Psi_*$-Operator in Ideal m-Spaces, Bol. Soc. Paran. Mat. 30 (2012), 53–66. https://doi.org/10.5269/bspm.v30i1.12787.
  18. A. Al-Omari, T. Noiri, On $Psi_mathcal{G}$-Operator in Grill Topological Spaces, Ann. Univ. Oradea Fasc. Mat. 19 (2012), 187–196.
  19. F.Y. Issaka, M. "{O}zkoç, On $Psi_delta$-Sets and $Psi_delta$-Functions Defined by Ideals, Poincare J. Anal. Appl. 8 (2021), 209–223. https://doi.org/10.46753/pjaa.2021.v08i01(i).020.
  20. M. Shahbaz, T. Kamran, U. Ishtiaq, M. Imtiaz, I. Popa, et al., Some New Notions of Continuity in Generalized Primal Topological Space, Mathematics 12 (2024), 3995. https://doi.org/10.3390/math12243995.
  21. S. Modak, Topology on Grill-Filter Space and Continuity, Bol. Soc. Parana. Mat. 31 (2013), 219–230. https://doi.org/10.5269/bspm.v31i2.16603.
  22. N. Levine, Semi-Open Sets and Semi-Continuity in Topological Spaces, Am. Math. Mon. 70 (1963), 36–41. https://doi.org/10.1080/00029890.1963.11990039.
  23. O. Njastad, On Some Classes of Nearly Open Sets, Pac. J. Math. 15 (1965), 961–970. https://doi.org/10.2140/pjm.1965.15.961.
  24. A.S. Mashhour, On Precontinuous and Weak Precontinuous Mappings, Proc. Math. Phys. Soc. Egypt 53 (1982), 47–53.
  25. M.E. Abd El-Monsef, $beta$-Open Sets and $beta$-Continuous Mappings, Bull. Fac. Sci. Assiut Univ. 12 (1983), 77–90.
  26. A. Al-Omari, T. Noiri, Decompositions of Continuity via Grills, Jordan J. Math. Stat. 4 (2011), 33–46.
  27. H.S. Alsaadi, M. Al-Hodieb, Sets Related to Openness and Continuity Decompositions in Primal Topological Spaces, Eur. J. Pure Appl. Math. 17 (2024), 1352–1368. https://doi.org/10.29020/nybg.ejpam.v17i2.5171.
  28. A.S. Mashhour, I.A. Hasanein, S.N. El-Deeb, $alpha$-Continuous and $alpha$-Open Mappings, Acta Math. Hung. 41 (1983), 213–218. https://doi.org/10.1007/bf01961309.
  29. S. Givant, P. Halmos, Introduction to Boolean Algebras, Springer, (2008).