Properties of H-almost continuous functions. (English) Zbl 0618.54013

The author considers some properties of the class of almost continuous functions between topological spaces, as defined by T. Husain [Pr. Mat. 10, 1-7 (1966; Zbl 0138.176)]. Such functions have been called nearly continuous by V. Pták [Bull. Soc. Math. Fr. 86, 41-74 (1958; Zbl 0082.325)], and precontinuous by A. S. Mashhour, M. E. Abd El-Monsef and S. El-Deeb [Proc. Math. Phys. Soc. Egypt 53, 47-53 (1982; Zbl 0571.54011)]. The author provides characterizations of almost continuous functions similar to those of Mashhour et al., investigates properties of these functions especially with respect to product spaces, and considers their relationship to rarely continuous functions.
Reviewer: I.L.Reilly


54C08 Weak and generalized continuity