Abstract
In [12], the authors give an explicit construction of the To ordered reflection of an ordered topological space (X, tau <=). All ordered topological spaces such that whose T-0-ordered reflections are T-1-ordered spaces are characterized. In this paper, some properties of the To ordered reflection of a given ordered topological space (X, tau, <=) are studies. The class of morphisms in ORDTOP orthogonal to all T-0-ordered topological space is characterized.