On $\mathrm{\infty }$-convex sets in spaces of scatteredly continuous functions

Given a topological space $X$, we study the structure of $\mathrm{\infty }$-convex subsets in the space $S{C}_p(X)$ of scatteredly continuous functions on $X$. Our main result says that for a topological space $X$ with countable strong fan tightness, each potentially bounded $\mathrm{\infty }$-convex subset $F\subset S{C}_p(X)$ is weakly discontinuous in the sense that each non-empty subset $A\subset X$ contains an open dense subset $U\subset A$ such that each function $f\mathrm{\mid }U$, $f\in F$,iscontinuous\mathrm{.}Thisimpliesthat$F$hasnetworkweight$nw(F)\le nw(X)$.