THE OSCILLATION OF QUASI-CONTINUOUS FUNCTIONS ON PAIRWISE ATTAINABLE SPACES

We introduce a class of attainable and pairwise attainable spaces which includes metrizable spaces. On this classes we develop a new technique of constructing of functions with given oscillations. We characterize the oscillations of quasi-continuous functions and alpha-separately continuous functions. In particular, we prove that the function g defined on a pairwise attainable space is the oscillation of some quasi-continuous function f if and only if g is nonnegative upper semi-continuous function with a meager support.