On RG-spaces and the regularity degree

Authors

  • R. Raphael Concordia University
  • R.G. Woods University of Manitoba

DOI:

https://doi.org/10.4995/agt.2006.1934

Keywords:

P-space, Almost-P space, Prime z-ideal, RG-space, Very weak P-point

Abstract

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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Author Biographies

R. Raphael, Concordia University

Mathematics and Statistics

R.G. Woods, University of Manitoba

Mathematics

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How to Cite

[1]
R. Raphael and R. Woods, “On RG-spaces and the regularity degree”, Appl. Gen. Topol., vol. 7, no. 1, pp. 73–101, Apr. 2006.

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Regular Articles