Shells, sequences and intersections

Abstract

In this paper we consider two facts concerning shells. First, we deal with ?nested? (decreasing or increasing) sequences of shells. We prove that the intersection, as well as the closure of the union of these sequences, is a shell. Secondly, we consider some questions raised in a paper by Stiles on shells, published half century ago. He left open some questions, also connected with ?spheres? (boundaries of balls), and with a finite intersection property. Here we give a new result on these problems.