The upwards-looking topology which was introduced by Adji and
Raeburn  corresponds to the hull-kernel topology in the primitive
ideal space $\Prim\te(\Gamma)$ of Toeplitz algebra $\te(\Gamma)$
of totally ordered abelian group $\Gamma$. In this paper we
discuss the closed sets in  $\Prim\te(\Gamma)$ with the
upwards-looking topology and characterize maximal primitive
ideals.