The SECQ, linear regularity, and the strong chip for an infinite system of closed convex sets in normed linear spaces

We consider a (finite or infinite) family of closed convex sets with nonempty intersection in a normed space. A property relating their epigraphs with their intersection's epigraph is studied, and its relations to other constraint qualifications ( such as the linear regularity, the strong CHIP, and Jameson's ( G)- property) are established. With suitable continuity assumption we show how this property can be ensured from the corresponding property of some of its finite subfamilies.