ON QUASI-UNIFORM CONVERGENCE OF SEQUENCES OF s1-STRONGLY QUASI-CONTINUOUS FUNCTIONS ON Rm.

A function ƒ : Rm → R is called s1-strongly quasi-continuous at a point X ∈ Rm if for each real ε > 0 and for each set A ∋ x belonging to the density topology, there is a nonempty open set V such that Ø ≠ A ∩ V ⊂ ƒ-1((ƒ(x) - ε, ƒ(x)) ∩ C(ƒ), where C(ƒ) denotes the set of continuity points of ƒ. It is proved that every λ-almost everywhere continuous function ƒ : Rm → R is the quasi-uniform limit of a sequence of s1-strongly quasi-continuous functions and that each measurable function ƒ : Rm → R is the quasi-uniform limit of a sequence of approximately quasi-continuous functions ƒ : Rm → R. [ABSTRACT FROM AUTHOR]