On some properties of $T_0$-ordered reflection

Abstract

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.

Keywords

• ordered topological space
• T2−ordered
• T1−ordered
• T0 −ordered
• ordered reflection
• ordered quotient
• category and functor.