Abstract. It is well known that the Helly dimension of the direct sum of convex sets is the maximum of the Helly dimension of the summands. In this paper we shall investigate the Helly dimension of the $L_1$-sum of two centrally symmetric compact convex sets. In case of the $L_1$-sum, the Helly dimension is not determined by the Helly dimension of the summands. Our main result is to give sharp bounds for the Helly dimension of the $L_1$-sum depending on the Helly dimension of the summands.

AMS Subject Classification (1991): 52A35, 52B35

Keyword(s): convex sets, Helly dimension, $L_1$-norm

Received April 20, 2009, and in revised form June 22, 2009. (Registered under 50/2009.)