Probabilistic convergence spaces and generalized metric spaces

Probabilistic convergence spaces and generalized metric spaces

The category PPRS(Δ), whose objects are probabilistic pretopological spaces which satisfy an axiom (Δ) and whose morphisms are continuous mappings, is introduced. Categories consisting of generalized metric spaces as objects and contraction mappings as morphisms are embedded as full subcategories of...

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Bibliographic Details
Main Author: Paul Brock
Format: Article
Language:English
Published: Wiley 1998-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Generalized metric space
probabilistic convergence space
t-norm
diagonal axiom
functor
isomorphism.
Online Access:http://dx.doi.org/10.1155/S0161171298000611
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Summary:The category PPRS(Δ), whose objects are probabilistic pretopological spaces which satisfy an axiom (Δ) and whose morphisms are continuous mappings, is introduced. Categories consisting of generalized metric spaces as objects and contraction mappings as morphisms are embedded as full subcategories of PPRS(Δ). The embeddings yield a description of metric spces and their most natural generalizations entirely in terms of convergence criteria.
ISSN:0161-1712
1687-0425

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