On Discrete Limits of Sequences of Bilaterally Quasicontinuous, Baire 1 Functions

Abstract

In this article we show that for the discrete limit $f$ of sequence of bilaterally quasicontinuous Baire 1 functions the complement of the set of all points at which $f$ is bilaterally quasicontinuous and has Darboux property, is nowhere dense. Moreover, a construction is given of a bilaterally quasicontinuous function which is the discrete limit of a sequence of Baire 1 functions, but is not the discrete limit of any sequence of bilaterally quasicontinuous Baire 1 functions.