Uniform limits of ${\mathcal{B}}_1^{\ast \ast }$-functions

We characterise the class of uniform limits of functions from Pawlak’s class ${\mathcal{B}}_1^{\ast \ast }$. The resulting class $u{\mathcal{S}}_1$, which contains functions with the oscillation rank one, is discussed in connection with its linear span. We apply a general, topological space, setting in our discussion.