On RG-spaces and the regularity degree

• Raphael, R. ^[1] ; Woods, R.G. ^[2]
  1. [1] Concordia University

     Concordia University

     Canadá

     
  2. [2] University of Manitoba

     University of Manitoba

     Canadá

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 7, Nº. 1, 2006, págs. 73-101
• Idioma: inglés
• DOI: 10.4995/agt.2006.1934
• Enlaces
  • Texto completo
• Resumen

  • We continue the study of a lattice-ordered ring G(X), associated with the ring C(X). Following, X is called RG when G(X) = C(Xδ). An RG-space must have a dense set of very weak P-points. It must have a dense set of almost-P-points if Xδ is Lindelöf, or if the continuum hypothesis holds and C(X) has small cardinality. Spaces which are RG must have finite Krull dimension when taken with respect to the prime z-ideals of C(X). There is a notion of regularity degree defined via the functions in G(X). Pseudocompact spaces and metric spaces of finite regularity degree are characterized.

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