Compactification of closed preordered spaces

• Minguzzi, E. ^[1]
  1. [1] University of Florence

     University of Florence

     Firenze, Italia

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 13, Nº. 2, 2012, págs. 207-223
• Idioma: inglés
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• Resumen

  • A topological preordered space admits a Hausdorff T2-preorder compactification if and only if it is Tychonoff and the preorder is represented by the family of continuous isotone functions. We construct the largest Hausdorff T2-preorder compactification for these spaces and clarify its relation with Nachbin’s compactification. Under local compactness the problem of the existence and identification of the smallest Hausdorff T2-preorder compactification is considered.