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Probablistic convergence spaces and regularity

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  • P. Brock
  • D. C. Kent

Abstract

The usual definition of regularity for convergence spaces can be characterized by a diagonal axiom R due to Cook and Fischer. The generalization of R to the realm of probabilistic convergence spaces depends on a t -norm T, and the resulting axiom R T defines T-regularity, which is the primary focus of this paper. We give several characterizations of T-regularity, both in general and for specific choices of T, and investigate some of its basic properties.

Suggested Citation

  • P. Brock & D. C. Kent, 1997. "Probablistic convergence spaces and regularity," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 20, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:417958
    DOI: 10.1155/S0161171297000896
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