Core compactness and diagonality in spaces of open sets

• Jordan, Francisco ^[1] ; Mynard, Frédéric ^[2]
  1. [1] Queensborough Community College, CUNY

     Queensborough Community College, CUNY

     Estados Unidos

     
  2. [2] Georgia Southern University

     Georgia Southern University

     Estados Unidos

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 12, Nº. 2, 2011, págs. 143-162
• Idioma: inglés
• DOI: 10.4995/agt.2011.1648
• Enlaces
  • Texto completo
• Resumen

  • We investigate when the space OX of open subsets of a topological space X endowed with the Scott topology is core compact. Such conditions turn out to be related to infraconsonance of X, which in turn is characterized in terms of coincidence of the Scott topology of OX × OX with the product of the Scott topologies of OX at (X,X). On the other hand, we characterize diagonality of OX endowed with the Scott convergence and show that this space can be diagonal without being pretopological. New examples are provided to clarify the relationship between pretopologicity, topologicity and diagonality of this important convergence space.

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