On some properties of $T_0$-ordered reflection


  • Sami Lazaar University Tunis-El Manar
  • Abdelouaheb Mhemdi University Tunis-El Manar




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


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.


Download data is not yet available.


A. Ayache, O. Echi, The envelope of a subcategory in Topology and group theory, Int. J. Math. Math. Sci. 21 (2005), 3787-3404.

K. Belaid, O. Echi and S. Lazaar, $T_{(alpha , beta )$-spaces and the Wallman compactification, Int. J. Math. Math. Sc. 68 (2004), 3717-3735.


C. Casacuberta, A. Frei and G. C. Tan, Extending localization functors, J. Pure Appl. Algebra 103 (1995), 149-165.


A. Deleanu, A. Frei, and P. Hilton, Generalized Adams completion, Cah. Topologie Géom. Différ. Catég.15 (1974), 61-82.

R. El Bashir and J. Velebil, Simultaneously reflective and coreflective subcategories of presheaves, Theory Appl. Categ. 10 (2002), 410-423.

A. Frei, On completion and shape, Bol. Soc. Brasil. Mat. 5 (1974), 147-159.


P. J. Freyd and G. M. Kelly, Categories of continuous functors (I), J. Pure Appl. Algebra, 2 (1972), 169-191. (http://dx.doi.org/10.1016/0022-4049(72)90001-1)

A. Grothendieck and J. Dieudonné, Eléments de géométrie algébrique, Springer-Verlag (1971).

J. M. Harvey, Reflective subcategories, Ill. J. Math. 29 (1985), 365-369.

H. Herrlich and G. Strecker, Categorical topology-Its origins as exemplified by the unfolding of the theory of topological reflections and coreflections before 1971, in Handbook of the History of General Topology, C.E. Aull and R. Lowen (eds.), Volume 1, Kluwer Academic Publishers, (1997), 255-341. (http://dx.doi.org/10.1007/978-94-017-0468-7_15)

H. Herrlich and G. Strecker, H-closed spaces and reflective subcategories, Math. Ann. 177 (1968), 302-309. (http://dx.doi.org/10.1007/BF01350722)

H-P. A. Künzi and T. A. Richmond, $T_i$-ordered reflections, Appl. Gen. Topol. 6, no. 2 (2005), 207-216.

H-P. A. Künzi, A. E. Mccluskey and T. A. Richmond, Ordered separation axioms and the Wallman ordered compactification, Publ. Math. Debrecen 73/3-4 (2008), 361-377.

S. Mac Lane, Categories for the Working Mathematician, Graduate Texts in Math. vol. 5, Springer-Verlag, New York, (1971). (http://dx.doi.org/10.1007/978-1-4612-9839-7)

W. Tholen, Reflective subcategories, Topology Appl. 27 (1987), 201-212.





How to Cite

S. Lazaar and A. Mhemdi, “On some properties of $T_0$-ordered reflection”, Appl. Gen. Topol., vol. 15, no. 1, pp. 43–54, Apr. 2014.