Ti-ordered reflections

• Künzi, Hans-Peter A. ^[1] ; Richmond, Thomas A. ^[2]
  1. [1] University of Cape Town

     University of Cape Town

     City of Cape Town, Sudáfrica

     
  2. [2] Western Kentucky University

     Western Kentucky University

     Estados Unidos

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 6, Nº. 2, 2005, págs. 207-216
• Idioma: inglés
• DOI: 10.4995/agt.2005.1955
• Enlaces
  • Texto completo
• Resumen

  • 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.

• Referencias bibliográficas
  • 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....
  • 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...
  • 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),...
  • D. D. Mooney and T. A. Richmond, Ordered quotients and the semilattice of ordered compactifications, Proceedings of the Tennessee Topology...
  • L. Nachbin, “Topology and Order”, Van Nostrand Math. Studies 4, Princeton, N.J.,(1965).