Existence of equilibrium in an abstract economy without $SS$-convexity

In this paper, we introduce the concept of $\mathrm{\Delta }$-convexity in an abstract economy with all choice sets being general topological spaces. We give a new generalization of the classical Yannelis-Prabhakar equilibrium existence theorem in abstract economies by relaxing $SS$-convexity to $\mathrm{\Delta }$-convexity.