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In [12], the authors give an explicit construction of the T0−ordered reflection of an ordered topological space (X, τ,≤) . All ordered topological spaces such that whose T0−ordered reflections are T1−ordered spaces are characterized. In this paper, some properties of the T0−ordered reflection of a given ordered topological space (X, τ,≤)  are studies. The class of morphisms in ORDTOP orthogonal to all T0−ordered topological space is characterized

On some properties of $T_0$-ordered reflection