T-regular probabilistic convergence spaces

    Authors

    J. Minkler; G. Minkler;G. Richardson

    Comments

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    Abbreviated Journal Title

    J. Aust. Math. Soc. A-Pure Math. Stat.

    Keywords

    convergence space; probabilistic convergence space; T-regular space; Mathematics; Statistics & Probability

    Abstract

    A probabilistic convergence structure assigns a probability that a given filter converges to a given element of the space. The role of the t-norm (triangle norm) in the study of regularity of probabilistic convergence spaces is investigated. Given a probabilistic convergence space, there exists a finest T-regular space which is coarser than the given space, and is referred to as the 'T-regular modification'. Moreover, for each probabilistic convergence space, there is a sequence of spaces, indexed by nonnegative ordinals, whose first term is the given space and whose last term is its T-regular modification. The T-regular modification is illustrated in the example involving 'convergence with probability lambda' for several t-norms. Suitable function space structures in terms of a given t-norm are also considered.

    Journal Title

    Journal of the Australian Mathematical Society Series a-Pure Mathematics and Statistics

    Volume

    64

    Publication Date

    1-1-1998

    Document Type

    Article

    Language

    English

    First Page

    210

    Last Page

    221

    WOS Identifier

    WOS:000073643300006

    ISSN

    0263-6115

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