Ti-ordered reflections


  • Hans-Peter A. Künzi University of Cape Town
  • Thomas A. Richmond Western Kentucky University




Ordered topological space, T2-ordered, T1-ordered, T0-ordered, Ordered reflection, Ordered quotient


We present a construction which shows that the Ti-ordered reflection (i ϵ {0, 1, 2}) of a partially ordered topological space (X, , τ, ≤) exists and is an ordered quotient of (X, τ, ≤). We give an explicit construction of the T0-ordered reflection of an ordered topological space (X, τ, ≤), and characterize ordered topological spaces whose T0-ordered reflection is T1-ordered.


Download data is not yet available.

Author Biographies

Hans-Peter A. Künzi, University of Cape Town

Department of Mathematics and Applied Mathematics

Thomas A. Richmond, Western Kentucky University

Department of Mathematics


K. Belaid, O. Echi, and S. Lazaar, T(α,β)-spaces and the Wallman compactification, Internat. J. Math. & Math. Sci. 2004 (68) (2004), 3717–3735. http://dx.doi.org/10.1155/S0161171204404050

A. S. Davis, Indexed systems of neighborhoods for general topological spaces, Am. Math. Monthly 68 (9) (1961), 886–893. http://dx.doi.org/10.2307/2311686

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

D. C. Kent, On the Wallman order compactification, Pacific J. Math. 118 (1985), 159–163. http://dx.doi.org/10.2140/pjm.1985.118.159

D. C. Kent and T. A. Richmond, Separation properties of the Wallman ordered compactification, Internat. J. Math. & Math. Sci. 13 (2) (1990), 209–222. http://dx.doi.org/10.1155/S0161171290000321

D. D. Mooney and T. A. Richmond, Ordered quotients and the semilattice of ordered compactifications, Proceedings of the Tennessee Topology Conference, P. R. Misra and M. Rajagopalan (eds.), World Scientific Inc., 1997, 141–155.

L. Nachbin, “Topology and Order”, Van Nostrand Math. Studies 4, Princeton, N.J.,(1965).


How to Cite

H.-P. A. Künzi and T. A. Richmond, “Ti-ordered reflections”, Appl. Gen. Topol., vol. 6, no. 2, pp. 207–216, Oct. 2005.



Regular Articles