Almost weakly continuous functions.

*(English)*Zbl 0789.54014N. Levine [Am. Math. Mon. 68, 44-46 (1961; Zbl 0100.186)] introduced the notion of a weakly continuous function between topological spaces. T. Husain [Prace Mat. 10, 1-7 (1966; Zbl 0138.176)] introduced and studied the notion of almost continuous functions. In [A. S. Mashhour, I. A. Hasanein, S. N. El-Deeb, Indian J. Pure Appl. Math. 13, 1119-1123 (1982; Zbl 0499.54009)] almost continuity is called precontinuity. Recently, D. S. Janković [Int. J. Math. Math. Sci. 8, 615-619 (1985; Zbl 0577.54012)] has introduced the notion of almost weakly continuous functions. Almost weak continuity is implied by both almost continuity and weak continuity which are independent of each other.

The purpose of the present paper is to obtain several characterizations of almost weakly continuous functions and to improve some of results established by Mashhour et al. [loc. cit.] and the first author [Bull. Math. Soc. Sci. Math. Répub. Soc. Roum., Nouv. Ser. 31(79), 163-168 (1987; Zbl 0618.54013)].

The purpose of the present paper is to obtain several characterizations of almost weakly continuous functions and to improve some of results established by Mashhour et al. [loc. cit.] and the first author [Bull. Math. Soc. Sci. Math. Répub. Soc. Roum., Nouv. Ser. 31(79), 163-168 (1987; Zbl 0618.54013)].

##### MSC:

54C08 | Weak and generalized continuity |