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On Contra $\pi gs$-Continuity

Year 2024, , 131 - 144, 24.09.2024

Nebiye Korkmaz

https://doi.org/10.36753/mathenot.1469064

Abstract

In this work, a novel form of contra continuity entitled as contra $\pi gs$-continuity is examined, which has connections to $\pi gs$-closed sets. Furthermore, correlations between contra $\pi gs$-continuity and several previously established forms of contra continuous functions are further explored, as well as basic features of contra $\pi gs$-continuous functions are disclosed.

Keywords

$\pi gs$-closed sets Contra $\pi gs$-continuity Contra continuity

References

  • [1] Levine, N.: Semi-open sets and semi-continuity in topological spaces. The American Mathematical Monthly. 70, 36-41 (1963).
  • [2] Levine, N.: Generalized closed sets in topology. Rendiconti del Circolo Matematico di Palermo. 19, 89-96 (1970).
  • [3] Dontchev, J., Noiri, T.: Quasi-normal and g-closed sets. Acta Mathematica Hungarica. 89(3), 211-9 (2000).
  • [4] Aslim, G., Caksu Guler, A., Noiri, T.: On gs-closed sets in topological spaces. Acta Mathematica Hungarica. 112(4), 275-283 (2006).
  • [5] Ganster, M., Reilly, I.L.:Locally closed sets and LC-continuous functions. International Journal of Mathematics and Mathematical Sciences. 3, 417-24 (1989).
  • [6] Dontchev, J.: Contra-continuous functions and strongly S-closed spaces. International Journal of Mathematics and Mathematical Sciences. 19(2), 303-10 (1996).
  • [7] Ekici, E.: On contra g-continuous functions. Chaos, Solitons & Fractals. 35(1), 71-81 (2008).
  • [8] Caldas, M., Jafari, S., Viswanathan, K., Krishnaprakash, S.: On contra gp-continuous functions. Kochi Journal of Mathematics. 5, 67-78 (2010).
  • [9] Dontchev, J., Noiri, T.: Contra-semicontinuous functions. Mathematica Pannonica. 10, 159-68 (1999).
  • [10] Stone, M. H.: Applications of the theory of Boolean rings to general topology. Transactions of the American Mathematical Society. 41, 375-481 (1937).
  • [11] Velicko, N.V.: H-closed topological spaces. American Mathematical Society Translations. 78, 103-18 (1968).
  • [12] Crossley, S.G., Hildebrand, S.K.: Semi topological properties. Fundamenta Mathematicae. 74, 233-254 (1972).
  • [13] Ekici, E.: On e-open sets and (D; S)-sets. Mathematica Moravica. 13(1), 29-36 (2009).
  • [14] Farhan, A.M., Yang, X.S.: New types of strongly continuous functions in topological spaces via - -open sets. European Journal of Pure and Applied Mathematics. 8(2), 185-200 (2015).
  • [15] El Maghrabi, A.I., Nasef, A. A.: Some classes of compactness and connectedness in terms of generalized closed sets. Journal of the Egyptian Mathematical Society. 13(1), 19-26 (2005).
  • [16] Özkoç, M., Şaşmaz, P.: On contra we-continuous functions. Poincare Journal of Analysis & Applications. 8-1(I), 51-65 (2021).
  • [17] Andrevic, D.:On b-open sets. Matematicki Vesnik. 48, 59-64 (1996).
  • [18] Dontchev, J., Przemski, M.: On the various decompositions of continuous and some weakly continuous functions. Acta Mathematica Hungarica. 71(1-2), 109-20 (1996).
  • [19] El Atik, A. A.: A study of some types of mappings on topological spaces. Msc thesis. Tanta University. (1997).
  • [20] Ravi, O., Rajasekaran, I., Murugesan, S., Pandi, A.: Contra g-continuous functions. Journal of Informatics and Mathematical Sciences. 6(2), 109–121 (2014).
  • [21] Sreeja, D., Janaki, C.: On gb-closed sets in topological spaces. International Journal of Mathematical Archive. 2(8), 1314-1320 (2011).
  • [22] Mashhour, A. S., Abd El-Monsef, M. E., El-Deeb, S. N.: On precontinuous and weak precontinuous mappings. Proceedings of the Mathematical and Physical Society of Egypt. 53, 47-53 (1982).
  • [23] Veera Kumar, M. K. R. S.: ^g-closed sets and GLC functions. Indian Journal of Mathematics. 43(2), 231-247 (2001).
  • [24] Subasree, R., Maria Singam, M.: On bˆg-closed sets in topological spaces. International Journal of Mathematical Archive. 4(7), 168-173 (2013).
  • [25] Subasree, R., Maria Singam, M.: On contra bˆg-continuous functions in topological spaces. International Journal of Mathematical Archive. 5(12), 66-74 (2014).
  • [26] Bala Deepa Arasi, K., Navaneetha Krishnan, S.: On sbˆg-closed sets in topological spaces. International Journal of Mathematical Archive. 6(10), 115-121 (2015).
  • [27] Zaitsev, V.: On certain classes of topological spaces and their bicompactifications. Doklady Akademii Nauk SSSR. 178, 778-9 (1968).
  • [28] Arya, S.P., Nour, T.: Characterizations of s-normal spaces. Indian Journal of Pure and Applied Mathematics. 21(8), 717-719 (1990).
  • [29] Park, J.H., Son, M. J., Lee, B. Y.: On gp-closed sets in topological spaces. Indian Journal of Pure and Applied Mathematics. (In press).
  • [30] Staum, R.: The algebra of bounded continuous functions into a nonarchimedean field. Pacific Journal of Mathematics. 50, 169-85 (1974).
  • [31] Njastad, O.: On some classes of nearly open sets. Pacific Journal of Mathematics. 15, 961-70 (1965).
  • [32] Abd El-Monsef, M. E., El-Deeb, S. N., Mahmoud, R. A.: -open sets and -continuous mappings. Bulletin of the Faculty of Science, Assiut University. 12(1), 77-90 (1983).
  • [33] Andrevic, D.: Semi-preopen sets. Matematicki Vesnik. 38(1), 24-32 (1986).
  • [34] Mrsevic, M.: On pairwise R and pairwise R 1 bitopological spaces. Bull. Math. Soc. Sci. Math. R. S. Roumanie. 30, 141-8 (1986).
  • [35] Ekici, E.: On a weaker form of RC-continuity. Analele Univ. Vest din Timisoara, Seria Matematica-Informatica. XLII(fasc. 1), 79-91 (2004).
  • [36] Noiri, T.: Super-continuity and some strong forms of continuity. Indian Journal of Pure and Applied Mathematics. 15, 241-50 (1984).
  • [37] Levine, N.: Strong continuity in topological spaces. The American Mathematical Monthly. 67, 269 (1960).
  • [38] Jafari, S., Noiri, T.: Contra-super-continuous functions. Annales Universitatis Scientiarium Budapestinensis de Rolando Eötvös Nominatae Sectio Mathematica. 42, 27-34 (1999).
  • [39] Caldas. M., Jafari, S., Noiri, T., Simoes, M.: A new generalization of contra-continuity via Levine’s g-closed sets. Chaos, Solutions & Fractals. 32(4), 1597-1603 (2007).
  • [40] Özkoç, M., Ayhan, B.S.: On contra e-continuous functions. Divulgaciones Matemáticas. 19(2), 1-13 (2018).
  • [41] Ekici, E.: New forms of contra continuity. Carpathian Journal of Mathematics. 24(1), 37-45 (2008).
  • [42] Özkoç, M., Ayhan, B. S.: On almost contra e-continuous functions. Jordan Journal of Mathematics and Statistics. 11(4), 383-408 (2018).
  • [43] Bala Deepa Arasi, K., Navaneetha Krishnan, S., Pious Missier, S.: On contra sbˆg-continuous functions in topological spaces. International Journal of Engineering Research & Technology. 5(2), 135-142 (2016).
  • [44] Arya, S.P., Gupta, R.: On strongly continuous mappings. Kyungpook Mathematical Journal. 14, 131-43 (1974).
  • [45] Bourbaki, N.: General Topology, Part I. Addison Wesley, Reading, MA, 1966.
  • [46] Jafari, S., Noiri, T.: Contra -continuous functions between topological spaces. Iran Int. J. Sci. 2(2), 153-67 (2001).
  • [47] Caldas, M., Jafari, S.: Some properties of contra -continuous functions. Memoirs of the Faculty of Science. Mathematics. Kochi University. 22, 19-28 (2001).
  • [48] Ekici, E.: On contra-continuity. Ann. Univ. Sci. Budapest. 47, 127-37 (2004).
  • [49] Soundararajan T.: Weakly Hausdorff spaces and the cardinality of topological spaces. In: Proceedings of the Kanpur Topological Conference, General Topology and Its Relations to Modern Analysis and Algebra, 1968, Prague. Academia Publishing House of the Czechoslovak Academy of Sciences, 301-306 (1971).

Year 2024, , 131 - 144, 24.09.2024

Nebiye Korkmaz

https://doi.org/10.36753/mathenot.1469064

Abstract

References

  • [1] Levine, N.: Semi-open sets and semi-continuity in topological spaces. The American Mathematical Monthly. 70, 36-41 (1963).
  • [2] Levine, N.: Generalized closed sets in topology. Rendiconti del Circolo Matematico di Palermo. 19, 89-96 (1970).
  • [3] Dontchev, J., Noiri, T.: Quasi-normal and g-closed sets. Acta Mathematica Hungarica. 89(3), 211-9 (2000).
  • [4] Aslim, G., Caksu Guler, A., Noiri, T.: On gs-closed sets in topological spaces. Acta Mathematica Hungarica. 112(4), 275-283 (2006).
  • [5] Ganster, M., Reilly, I.L.:Locally closed sets and LC-continuous functions. International Journal of Mathematics and Mathematical Sciences. 3, 417-24 (1989).
  • [6] Dontchev, J.: Contra-continuous functions and strongly S-closed spaces. International Journal of Mathematics and Mathematical Sciences. 19(2), 303-10 (1996).
  • [7] Ekici, E.: On contra g-continuous functions. Chaos, Solitons & Fractals. 35(1), 71-81 (2008).
  • [8] Caldas, M., Jafari, S., Viswanathan, K., Krishnaprakash, S.: On contra gp-continuous functions. Kochi Journal of Mathematics. 5, 67-78 (2010).
  • [9] Dontchev, J., Noiri, T.: Contra-semicontinuous functions. Mathematica Pannonica. 10, 159-68 (1999).
  • [10] Stone, M. H.: Applications of the theory of Boolean rings to general topology. Transactions of the American Mathematical Society. 41, 375-481 (1937).
  • [11] Velicko, N.V.: H-closed topological spaces. American Mathematical Society Translations. 78, 103-18 (1968).
  • [12] Crossley, S.G., Hildebrand, S.K.: Semi topological properties. Fundamenta Mathematicae. 74, 233-254 (1972).
  • [13] Ekici, E.: On e-open sets and (D; S)-sets. Mathematica Moravica. 13(1), 29-36 (2009).
  • [14] Farhan, A.M., Yang, X.S.: New types of strongly continuous functions in topological spaces via - -open sets. European Journal of Pure and Applied Mathematics. 8(2), 185-200 (2015).
  • [15] El Maghrabi, A.I., Nasef, A. A.: Some classes of compactness and connectedness in terms of generalized closed sets. Journal of the Egyptian Mathematical Society. 13(1), 19-26 (2005).
  • [16] Özkoç, M., Şaşmaz, P.: On contra we-continuous functions. Poincare Journal of Analysis & Applications. 8-1(I), 51-65 (2021).
  • [17] Andrevic, D.:On b-open sets. Matematicki Vesnik. 48, 59-64 (1996).
  • [18] Dontchev, J., Przemski, M.: On the various decompositions of continuous and some weakly continuous functions. Acta Mathematica Hungarica. 71(1-2), 109-20 (1996).
  • [19] El Atik, A. A.: A study of some types of mappings on topological spaces. Msc thesis. Tanta University. (1997).
  • [20] Ravi, O., Rajasekaran, I., Murugesan, S., Pandi, A.: Contra g-continuous functions. Journal of Informatics and Mathematical Sciences. 6(2), 109–121 (2014).
  • [21] Sreeja, D., Janaki, C.: On gb-closed sets in topological spaces. International Journal of Mathematical Archive. 2(8), 1314-1320 (2011).
  • [22] Mashhour, A. S., Abd El-Monsef, M. E., El-Deeb, S. N.: On precontinuous and weak precontinuous mappings. Proceedings of the Mathematical and Physical Society of Egypt. 53, 47-53 (1982).
  • [23] Veera Kumar, M. K. R. S.: ^g-closed sets and GLC functions. Indian Journal of Mathematics. 43(2), 231-247 (2001).
  • [24] Subasree, R., Maria Singam, M.: On bˆg-closed sets in topological spaces. International Journal of Mathematical Archive. 4(7), 168-173 (2013).
  • [25] Subasree, R., Maria Singam, M.: On contra bˆg-continuous functions in topological spaces. International Journal of Mathematical Archive. 5(12), 66-74 (2014).
  • [26] Bala Deepa Arasi, K., Navaneetha Krishnan, S.: On sbˆg-closed sets in topological spaces. International Journal of Mathematical Archive. 6(10), 115-121 (2015).
  • [27] Zaitsev, V.: On certain classes of topological spaces and their bicompactifications. Doklady Akademii Nauk SSSR. 178, 778-9 (1968).
  • [28] Arya, S.P., Nour, T.: Characterizations of s-normal spaces. Indian Journal of Pure and Applied Mathematics. 21(8), 717-719 (1990).
  • [29] Park, J.H., Son, M. J., Lee, B. Y.: On gp-closed sets in topological spaces. Indian Journal of Pure and Applied Mathematics. (In press).
  • [30] Staum, R.: The algebra of bounded continuous functions into a nonarchimedean field. Pacific Journal of Mathematics. 50, 169-85 (1974).
  • [31] Njastad, O.: On some classes of nearly open sets. Pacific Journal of Mathematics. 15, 961-70 (1965).
  • [32] Abd El-Monsef, M. E., El-Deeb, S. N., Mahmoud, R. A.: -open sets and -continuous mappings. Bulletin of the Faculty of Science, Assiut University. 12(1), 77-90 (1983).
  • [33] Andrevic, D.: Semi-preopen sets. Matematicki Vesnik. 38(1), 24-32 (1986).
  • [34] Mrsevic, M.: On pairwise R and pairwise R 1 bitopological spaces. Bull. Math. Soc. Sci. Math. R. S. Roumanie. 30, 141-8 (1986).
  • [35] Ekici, E.: On a weaker form of RC-continuity. Analele Univ. Vest din Timisoara, Seria Matematica-Informatica. XLII(fasc. 1), 79-91 (2004).
  • [36] Noiri, T.: Super-continuity and some strong forms of continuity. Indian Journal of Pure and Applied Mathematics. 15, 241-50 (1984).
  • [37] Levine, N.: Strong continuity in topological spaces. The American Mathematical Monthly. 67, 269 (1960).
  • [38] Jafari, S., Noiri, T.: Contra-super-continuous functions. Annales Universitatis Scientiarium Budapestinensis de Rolando Eötvös Nominatae Sectio Mathematica. 42, 27-34 (1999).
  • [39] Caldas. M., Jafari, S., Noiri, T., Simoes, M.: A new generalization of contra-continuity via Levine’s g-closed sets. Chaos, Solutions & Fractals. 32(4), 1597-1603 (2007).
  • [40] Özkoç, M., Ayhan, B.S.: On contra e-continuous functions. Divulgaciones Matemáticas. 19(2), 1-13 (2018).
  • [41] Ekici, E.: New forms of contra continuity. Carpathian Journal of Mathematics. 24(1), 37-45 (2008).
  • [42] Özkoç, M., Ayhan, B. S.: On almost contra e-continuous functions. Jordan Journal of Mathematics and Statistics. 11(4), 383-408 (2018).
  • [43] Bala Deepa Arasi, K., Navaneetha Krishnan, S., Pious Missier, S.: On contra sbˆg-continuous functions in topological spaces. International Journal of Engineering Research & Technology. 5(2), 135-142 (2016).
  • [44] Arya, S.P., Gupta, R.: On strongly continuous mappings. Kyungpook Mathematical Journal. 14, 131-43 (1974).
  • [45] Bourbaki, N.: General Topology, Part I. Addison Wesley, Reading, MA, 1966.
  • [46] Jafari, S., Noiri, T.: Contra -continuous functions between topological spaces. Iran Int. J. Sci. 2(2), 153-67 (2001).
  • [47] Caldas, M., Jafari, S.: Some properties of contra -continuous functions. Memoirs of the Faculty of Science. Mathematics. Kochi University. 22, 19-28 (2001).
  • [48] Ekici, E.: On contra-continuity. Ann. Univ. Sci. Budapest. 47, 127-37 (2004).
  • [49] Soundararajan T.: Weakly Hausdorff spaces and the cardinality of topological spaces. In: Proceedings of the Kanpur Topological Conference, General Topology and Its Relations to Modern Analysis and Algebra, 1968, Prague. Academia Publishing House of the Czechoslovak Academy of Sciences, 301-306 (1971).
There are 49 citations in total.

Details

Primary Language English
Subjects Applied Mathematics (Other)
Journal Section Articles
Authors

Nebiye Korkmaz 0000-0003-2248-4280

Early Pub Date June 27, 2024
Publication Date September 24, 2024
Submission Date April 16, 2024
Acceptance Date June 19, 2024
Published in Issue Year 2024

Cite

APA Korkmaz, N. (2024). On Contra $\pi gs$-Continuity. Mathematical Sciences and Applications E-Notes, 12(3), 131-144. https://doi.org/10.36753/mathenot.1469064
AMA Korkmaz N. On Contra $\pi gs$-Continuity. Math. Sci. Appl. E-Notes. September 2024;12(3):131-144. doi:10.36753/mathenot.1469064
Chicago Korkmaz, Nebiye. “On Contra $\pi Gs$-Continuity”. Mathematical Sciences and Applications E-Notes 12, no. 3 (September 2024): 131-44. https://doi.org/10.36753/mathenot.1469064.
EndNote Korkmaz N (September 1, 2024) On Contra $\pi gs$-Continuity. Mathematical Sciences and Applications E-Notes 12 3 131–144.
IEEE N. Korkmaz, “On Contra $\pi gs$-Continuity”, Math. Sci. Appl. E-Notes, vol. 12, no. 3, pp. 131–144, 2024, doi: 10.36753/mathenot.1469064.
ISNAD Korkmaz, Nebiye. “On Contra $\pi Gs$-Continuity”. Mathematical Sciences and Applications E-Notes 12/3 (September 2024), 131-144. https://doi.org/10.36753/mathenot.1469064.
JAMA Korkmaz N. On Contra $\pi gs$-Continuity. Math. Sci. Appl. E-Notes. 2024;12:131–144.
MLA Korkmaz, Nebiye. “On Contra $\pi Gs$-Continuity”. Mathematical Sciences and Applications E-Notes, vol. 12, no. 3, 2024, pp. 131-44, doi:10.36753/mathenot.1469064.
Vancouver Korkmaz N. On Contra $\pi gs$-Continuity. Math. Sci. Appl. E-Notes. 2024;12(3):131-44.

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