On some properties of $T_0$-ordered reflection

Sami Lazaar, Abdelouaheb Mhemdi

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.

Subject classification

54F05; 18B30; 54G20; 54C99; 06F30; 18A05.

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