Ti-ordered reflections
Submitted: 2013-11-25
|Accepted: 2013-11-25
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Keywords:
Ordered topological space, T2-ordered, T1-ordered, T0-ordered, Ordered reflection, Ordered quotient
Supporting agencies:
South African Research Foundation for partial financial support under Grant Number 2068799.
Abstract:
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.
References:
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).
