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Z-supercontinuous functions. (English) Zbl 1010.54012
Summary: A new class of functions, called \(z\)-supercontinuous functions, is introduced. Basic properties of \(z\)-supercontinuous functions are studied. Sufficient conditions on domain/range are given for a continuous function to be \(z\)-supercontinuous. The class of \(z\)-supercontinuous functions properly includes the class of clopen maps of I. L. Reilly and M. K. Vamanamurthy [Indian J. Pure Appl. Math. 14, 767-772 (1983; Zbl 0509.54007)]. Moreover, the class of \(z\)-supercontinuous functions constitutes a proper subclass of each of the classes of
(1) supercontinuous functions introduced by B. M. Munshi and D. S. Bassan [ibid. 13, 229-236 (1982; Zbl 0483.54007)];
(2) strongly \(\theta\)-continuous functions of T. Noiri [J. Korean Math. Soc. 16, 161-166 (1980; Zbl 0435.54010)];
(3) \(D\)-supercontinuous functions initiated by J. K. Kohli and Davinder Singh [Indian J. Pure Appl. Math. 32, No. 2, 227-235 (2001; Zbl 0977.54011)].

54C08 Weak and generalized continuity