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.

T0-reflection and some separation axioms in PRETOP

“…New separation axioms are presented in [2] in the category of Topological spaces. After that this concept is studied in different categories such as the category of ordered topological spaces in [8,9] and the category of generalized topological spaces in [11].…”

On the category of ordered pre-topological spaces

“…The study of T 0 -reflection was generalized to other categories. As examples we can cite the category of the ordered topological space ORDTOP in [14,15] (ordered topological spaces are presented by Nachbin in [18]), the category of the generalized topology GenTOP in [17], and the category of the pretopological spaces PreTOP in [1].…”

Functionally Separation Axioms on General Topology

“…On the other hand, some separation axioms were introduced using generalized open sets (see [7] and the references mentioned therein). Also, separation axioms have been generalized to other spaces in general topology like pretopological spaces, ordered topological spaces, and generalized topological spaces (see [8][9][10][11]). Another generalization of separation axioms was given using functions in the category of topological spaces (see [12]).…”