Title

T-regular probabilistic convergence spaces

Keywords

Convergence space; Probabilistic convergence space; T-regular space

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 λ' for several t-norms. Suitable function space structures in terms of a given t-norm are also considered.

Publication Date

1-1-1998

Publication Title

Journal of the Australian Mathematical Society

Volume

64

Issue

2

Number of Pages

210-221

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1017/s1446788700001701

Socpus ID

0040634993 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0040634993

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