On ∞-convex sets in spaces of scatteredly continuous functions

Given a topological space X, we study the structure of infinity-convex subsets in the space SCp(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 infinity-convex subset F subset of SCp(X) is weakly discontinuous in the sense that each non-empty subset A subset of X contains an open dense subset U subset of A such that each function f vertical bar U, f is an element of F, is continuous. This implies that F has network weight nw(F) <= nw(X). (C) 2014 Elsevier B.V. All rights reserved.