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$$D$$-supercontinuous functions. (English) Zbl 0977.54011
Summary: The notion of a $$D$$-supercontinuous function is introduced. Basic properties of $$D$$-supercontinuous functions are studied. The class of $$D$$-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)]. The notion of $$D$$-supercontinuous function is independent of the notion of a supercontinuous function introduced by B. M. Munshi and D. S. Bassan [ibid. 13, 229-236 (1982; Zbl 0483.54007)]. The behaviour of (completely) $$G_\delta$$-regular spaces under $$D$$-supercontinuous function is investigated.

##### MSC:
 54C05 Continuous maps 54C10 Special maps on topological spaces (open, closed, perfect, etc.)