On characterizations of weakly e*-continuity

• Burcu Sünbül Ayhan Turkish-German University Rectorship Department of Data Processing
• Murad Özkoç Muğla Sıtkı Koçman University Faculty of Science Department of Mathematics

Keywords: e*-open, weakly e*-continuity, almost e*-continuity, faintly e*-continuity

Abstract

The aim of this paper is to investigate some of the fundamental properties of weakly e*-continuous functions introduced by Ayhan and \"{O}zko\c{c} in [3]. Moreover, several characterizations and some properties concerning weakly e*-continuous functions are obtained. Then, we investigate relationships between weak e*-continuity and some other types of continuity. Also, we investigate the relationships between weakly e*-continuous functions and connectedness and graph of functions.

References

Abd El-Monsef, M. E.; El-Deeb, S. N. and Mahmoud, R. A.; β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12 (1983), 77–90.

Andrijević, D.; On b-open sets, Mat. Vesnik 48 (1996), 59–64.

Ayhan, B. S. and Özkoç, M.; Almost e*-continuous functions and their characterizations, J. Nonlinear Sci. Appl. 9 (2016), 6408–6423.

Ekici, E.; On a-open sets, A*-sets and decompositions of continuity and super-continuity, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 51 (2008), 39–51.

Ekici, E.; On e*-open sets and (D, S)*-sets, Math. Morav. 13(1) (2009), 29–36.

Ekici, E.; On e-open sets, DP*-sets and DPE*-sets and decompositions of continuity, Arabian J. Sci. Eng. 33(2A) (2008), 269–282.

Jafari, S. and Rajesh, N.; On faintly δ-β-continuous functions (submitted).

Levine, N.; A decomposition of continuity in topological spaces, Amer. Math. Monthly 68 (1961), 44–46.

Levine, N.; Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36–41.

Mashhour, A. S.; Abd El-Monsef, M. E. and El-Deeb, S. N.; On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53 (1982), 47–53.

Noiri, T.; On δ-continuous functions, J. Korean Math. Soc., 16(2) (1980), 161–166.

Özkoç, M. and Aslım, G.; On weakly e-continuous functions, Hacettepe J. Math. Stat. 40(6) (2011), 781–791.

Özkoç, M. and Atasever, K. S.; On some forms of e ∗ -irresoluteness, J. Linear Topol. Algebra, 08(1) (2019), 25–39.

Popa, V. and Noiri, T.; On weakly β-continuous functions, An. Univ. Timis. Ser. Mat.Inform. 32(2A) (1994), 83–92.

Şengül, U.; Weakly b-continuous functions, Chaos Solitons Fractals 41 (2009), 1070–1077.

Stone, M. H.; Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), 375–381.

Velic̆ko, N. V.; H-closed topological spaces, Amer. Math. Soc. Transl. 78(2) (1968), 103–118.