In a topological sup-semilattice, we established a new existence result for vector quasiequilibrium problems. By the analysis of essential stabilities of maximal elements in a topological sup-semilattice, we prove that for solutions of each vector quasi-equilibrium problem, there exists a connected minimal essential set which can resist the perturbation of the vector quasi-equilibrium problem.
Qi-Qing Song. "The Existence and Stability of Solutions for Vector Quasiequilibrium Problems in Topological Order Spaces." J. Appl. Math. 2013 (SI21) 1 - 6, 2013. https://doi.org/10.1155/2013/218402