ON βδs-IRRESOLUTE FUNCTIONS

Abstract

The purpose of the present paper is to introduce and investigate a new class of functions, namely αδs -irresolute functions. Several properties of these functions and a decomposition of αδs -irresoluteness are also given. References [1] M. Caldas, D. N. Georgiou, S. Jafari and T. Noiri, More on δ-semiopen sets, Note Mat., 22 (2003), 113-126. [2] M. Caldas and S. Jafari, On semi δs-irresolute functions, Fasc. Math., 58 (2017), 47-55. [3] G. I. Chae, T. Noiri and D. W. Lee, On na-continuous functions, Kyungpook Math. J., 26 (1986), 73-79. [4] B. Y. Lee, M. J. Son and J. H. Park, δ-semiopen sets and its applications, Far East J. Math. Sci. (FJMS), 3 (2001), 745-759. [5] N. Levine, Semi open sets and semi continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36-41. [6] S. N. Maheshwari and S. S. Thakur, On α-irresolute mappings, Tamkang J. Math., 11 (1980), 209-214. [7] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53 (1982), 47-53. [8] A. S. Mashhour, I. A. Hasanein and S. N. El-Deeb, α-continuous and α-open mappings, Acta Math. Hungar, 41 (1983), 213-218. [9] O. Nj̊astad, On some classes of nearly open sets, Pacific J. Math., 15 (1965), 961-970. [10] T. Noiri, Remarks on δ-semi-open sets and δ-preopen sets, Demonstratio Math., 36 (2003), 1007-1020. [11] J. H. Park, B. Y. Lee and M. J. Son, On δ-semiopen sets in topological spaces, J. Indian Acad. Math., 19 (1997), 59-67. [12] N. V. Veličko, H-closed topological spaces, Amer. Math. Soc. Transl. (2), 78 (1968), 103-118. Received 19 February 2019 1 Department of Mathematics, Faculty of Sciences, Selçuk University, Selçuklu, Konya, 42130 Turkey. 2 Shiokita-cho, Hinagu, Yatsushiro-shi, Kumamoto-ken, 869-5142 Japan. E-mail address: 1 [email protected], 2 [email protected] 2010 Mathematics Subject Classification. 54C08, 54C10, 54A05.