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Year 2024, Volume: 12 Issue: 3, 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).

On Contra $\pi gs$-Continuity

Year 2024, Volume: 12 Issue: 3, 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).
There are 49 citations in total.

Details

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

Nebiye Korkmaz 0000-0003-2248-4280

Submission Date April 16, 2024
Acceptance Date June 19, 2024
Early Pub Date June 27, 2024
Publication Date September 24, 2024
Published in Issue Year 2024 Volume: 12 Issue: 3

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 1.Korkmaz N. On Contra $\pi gs$-Continuity. Math. Sci. Appl. E-Notes. 2024;12(3):131-144. doi:10.36753/mathenot.1469064
Chicago Korkmaz, Nebiye. 2024. “On Contra $\pi Gs$-Continuity”. Mathematical Sciences and Applications E-Notes 12 (3): 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 [1]N. Korkmaz, “On Contra $\pi gs$-Continuity”, Math. Sci. Appl. E-Notes, vol. 12, no. 3, pp. 131–144, Sept. 2024, doi: 10.36753/mathenot.1469064.
ISNAD Korkmaz, Nebiye. “On Contra $\pi Gs$-Continuity”. Mathematical Sciences and Applications E-Notes 12/3 (September 1, 2024): 131-144. https://doi.org/10.36753/mathenot.1469064.
JAMA 1.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, Sept. 2024, pp. 131-44, doi:10.36753/mathenot.1469064.
Vancouver 1.Korkmaz N. On Contra $\pi gs$-Continuity. Math. Sci. Appl. E-Notes [Internet]. 2024 Sept. 1;12(3):131-44. Available from: https://izlik.org/JA67AB84BF

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