On some properties of $T_0$-ordered reflection

Sami Lazaar

Tunisia

University Tunis-El Manar

Abdelouaheb Mhemdi

Tunisia

University Tunis-El Manar

Submitted: 2014-02-17

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Accepted: 2014-02-17

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Published: 2014-04-01

DOI: https://doi.org/10.4995/agt.2014.2144
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Keywords:

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

Supporting agencies:

This research was not funded

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.
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