Minimal TUD spaces

• McCluskey, A.E. ^[1] ; Watson, W.S. ^[2]
  1. [1] National University of Ireland

     National University of Ireland

     Irlanda

     
  2. [2] York University (Canadá)

     York University (Canadá)

     Canadá

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 3, Nº. 1, 2002, págs. 55-64
• Idioma: inglés
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• Resumen

  • A topological space is TUD if the derived set of each point is the union of disjoint closed sets. We show that there is a minimal TUD space which is not just the Alexandroff topology on a linear order. Indeed the structure of the underlying partial order of a minimal TUD space can be quite complex. This contrasts sharply with the known results on minimality for weak separation axioms.