Abstract
A new class of functions called z-perfectly continuous functions is introduced,
which properly includes the class of pseudo perfectly continuous functions [24] but turns out to be independent of continuity. Besides the study of the basic properties of z-perfectly continuous functions and the interplay with topological properties, sufficient conditions are outlined for their function spaces to be closed, respectively compact, in the topology of pointwise convergence.
Cuvinte cheie
(pseudo) perfectly continuous function
z-supercontinuous function
z-continuous function
slightly continuous function
z–partition topology
functionally
Hausdorff space
Alexandroff space ( saturated space)