The Linear Regular of Infinitely Many Sets

This paper deals with bounded linear regularity and linear regularity of closed convex polyhedral sets and pseudo-convex sets. The linear regularity of an arbitrary collection of closed convex polyhedral subsets can be obtained under certain conditions. At the same time, the sufficient conditions are presented, which are for infinitely many polyhedral sets to be boundedly linearly regular and linearly regular. Some relevant examples are given in this paper. Finally, for infinitely many pseudo-convex sets, the linear regularity can be obtained.