We show that any uniformly continuous and convex compact valued Nemytskiĭ composition operator acting in the spaces of functions of bounded φ-variation in the sense of Riesz is generated by an affine function.

The paper deals with the existence of a quasi continuous selection of a multifunction for which upper inverse image of any open set with compact complement contains a set of the form $(G\setminus I)\cup J$, where $G$ is open and $I$, $J$ are from a given ideal. The methods are based on the properties of a minimal multifunction which is generated by a cluster process with respect to a system of subsets of the form $(G\setminus I)\cup J$.