Separation axioms in topological preordered spaces and the existence of continuous order-preserving functions

• Bosi, G. ^[1] ; Isler, R. ^[1]
  1. [1] University of Trieste

     University of Trieste

     Trieste, Italia

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 1, Nº. 1, 2000, págs. 93-98
• Idioma: inglés
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• Resumen

  • We characterize the existence of a real continuous order-preserving function on a topological preordered space, under the hypotheses that the topological space is normal and the preorder satisfies a strong continuity assumption, called IC-continuity. Under the same continuity assumption concerning the preorder, we present a sufficient condition for the existence of a continuous order-preserving function in case that the topological space is completely regular.