Mu-xi-I-open sets in ideal generalized topological spaces
DOI:
https://doi.org/10.5269/bspm.79780Abstract
In this paper, we introduce a new class of generalized-I-open sets namely, mu-xi-I-open sets and specifically, we focus the mu-beta-I-open sets. Further, we define the generalized-I-operators such as mu-xi-I-interior and mu-xi-I-closure and analyze the ideal generalized topological concepts through these operators. Moreover, we obtain the various types of ideal generalized continuous such as (mu-xi-I, nu)-continuous and (mu-xi-I, nu-xi-J)-continuous and discuss their relationships between them.
References
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\bibitem{d2} M. E. Abd El-Monsef, E. F. Lashien and A. A. Nasef, \emph{On $I$-open sets and $I$-continuous functions}, Kyungpook Math. J. 32 (1992), 21-30.
\bibitem{d3} A. Csaszar, \emph{Generalized open sets}, Acta Math. Hunger., 75 (1997), 65-87.
\bibitem{d4} A. Csaszar, \emph{On the $\gamma$-interior and $\gamma$-closure of a set}, Acta Math. Hungar., 80 (1998), 89-93.
\bibitem{d5} A. Csaszar, \emph{Generalized topology, generalized continuity}, Acta Math. Hungar., 96 (2002), 351-357.
\bibitem{d6} A. Csaszar, \emph{Generalized open sets in generalized topologies}, Acta Math. Hungar., 105 (2005), 53-66.
\bibitem{d7} A. Csaszar, \emph{Further remarks on the formula for $\gamma$-interior}, Acta Math. Hungar., 113 (2006), 325-332.
\bibitem{d8} A. Csaszar, \emph{Modifications of generalized topologies via hereditary classes}, Acta Math. Hungar., 115 (2007), 29-36.
\bibitem{d9} A. Csaszar, \emph{$\delta$ and $\theta$-modifications of generalized topologies}, Acta Math. Hungar., 120 (2008), 275-279.
\bibitem{d10} E. Hatir and T. Noiri, \emph{On decompositions of continuity via idealization}, Acta Math. Hungar., 96 (2002), 341-349.
\bibitem{d11} E. Hayashi, \emph{Topologies defined by local properties}, Math. Ann., 156 (1964), 205-215.
\bibitem{d12} D. Jankovic and T. R. Hamlett, \emph{New topologies from old via ideals}, Amer. Math. Monthly, 97 (1990), 295-310.
\bibitem{d13} K. Kuratowski, \emph{Topology 1}, Academic Press (New York, 1996).
\bibitem{d14} N. Levine, \emph{Semi-open sets and semi continuity in topological spaces}, Amer. Math. Monthly, 70 (1963), 36-41.
\bibitem{d15} N. Levine, \emph{Generalized closed sets in topology}, Rend. Circ. Mat. Palermo, 19 (1970), 89-96.
\bibitem{d16} A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, \emph{On precontinuous and weak precontinuous mappings}, Proc. Math. Phys. Soc. Egypt, 53 (1982), 47-53.
\bibitem{d17} S. Modak, \emph{Ideal on generalized topological spaces}, Scien. Magna, 11 (2016), 14-20.
\bibitem{d18} O. Njastad, \emph{On some classes of nearly open sets}, Pacific J. Math., 15 (1965), 961-970.
\bibitem{d19} T. Noiri and B. Roy, \emph{Unification of generalized open sets on topological spaces}, Acta. Math. Hungar., 130 (2011), 349-357.
\bibitem{d20} G. Sai Sundara Krishnan, D. Saravanakumar, M. Ganster and K. Balachandran, \emph{On a class of $\gamma^*$-pre-open sets in topological spaces}, Kyungpook Math. J., 54 (2014), 173-188.
\bibitem{d25} D. Saravanakumar, \emph{$\tilde{\gamma}$-open sets and ($\tilde{\gamma}$, $\tilde{\beta}$)-continuous mappings}, Bol. Soc. Paran. Mat., 41 (2023), 1-11.
\bibitem{d21} D. Saravanakumar, M. Ganster, N. Kalaivani and G. Sai Sundara Krishnan, \emph{On ($\gamma^*$, $\beta^*$)-almost-pre-continuous mappings in topological spaces}, J. Egypt. Math. Soc., 23 (2015), 180-189.
\bibitem{d22} D. Saravanakumar, N. Kalaivani and G. Sai Sundara Krishnan, \emph{Operations contra-pre-continuous mappings}, Int. J. Mat. Anal., 8 (2014), 219-227.
\bibitem{d23} D. Saravanakumar, N. Kalaivani and G. Sai Sundara Krishnan, \emph{$\tilde{\mu}$-open sets in generalized topological spaces}, Malaya J. Mat., 3 (2015), 268-276.
\bibitem{d24} D. Saravanakumar, N. Kalaivani and G. Sai Sundara Krishnan, \emph{Operations pre-continuous mappings in topological spaces}, Acta Sci. et Int., 2 (2018), 30-42.
\bibitem{d26} D. Saravanakumar and G. Sai Sundara Krishnan, \emph{Generalized mappings via new closed sets}, Int. J. Mat. Sci. Appl., 2 (2012), 127-137.
\bibitem{d27} D. Saravanakumar and T. Sathiyanandham, \emph{$(\tilde{\mu}, \tilde{\nu})$-continuous mappings in generalized topological spaces}, Int. J. Pure and App. Math., 113 (2017), 20-28.
\bibitem{d28} R. Shen, \emph{Remarks on products of generalized topologies}, Acta Math. Hungar.,124 (2009), 363-369.
\bibitem{d29} P. Sivagami, \emph{Remarks on $\gamma$-interior}, Acta Math. Hungar., 119 (2008), 81-94.
\bibitem{d30} R. Vaidyanathaswamy, \emph{The localization theory in set-topology}, Proc. Indian. Acad. Sci., 20 (1945), 51-61.
\bibitem{d31} N. V. Velicko, \emph{$H$-closed topological spaces}, Amer. Math. Soc. Transl., 78 (1968), 102-118.
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2026-06-05
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