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 also the intersection, or 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.