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