A problem of intersection of balls in normed space

This paper investigates the topological properties of intersections of balls in finite-dimensional normed spaces - a problem that naturally arises when constructing covers for estimating the Gromov-Hausdorff distance.

We study the topology of a set obtained by removing a large closed ball from a finite intersection of small open balls.

It is proved that in an arbitrary normed plane, such a set is always contractible, provided that it is non-empty.