Properties of Multi-Valued Functions - Charatonik, Włodzimierz; Michalik, Daria (Topology Proceedings, 2021)
For a given topological property $\mathcal{P}$ of mappings, we say that a multi-valued function $f: X \Rightarrow Y$ is $\operatorname{dir}-\mathcal{P}(\operatorname{co}-\mathcal{P})$ if the projection from the graph of $f$ to $Y$ (onto X ) has property $\mathcal{P}$. In this article, we investigate properties of $\operatorname{dir}-\mathcal{P}$ and $\operatorname{co}-\mathcal{P}$ functions. We discuss composition property, composition factor property, and product property of such functions.