The existence theorem of essential connected component in the paper [1] is improved. As an application, deduce the existence theorem of essential connected component of KKM point-sets id deduced.

• 我们对文献[1]中统-的本质连通区的存在性定理进行了改进，然后利用该定理导出KKM点集的本质连通区的存在性定理。