Probabilistic convergence spaces and generalized metric spaces

Paul Brock

International Journal of Mathematics and Mathematical Sciences, 1998, vol. 21, 1-14

Abstract:

The category P P R S ( 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 P P R S ( Δ ) . The embeddings yield a description of metric spces and their most natural generalizations entirely in terms of convergence criteria.

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:735395

DOI: 10.1155/S0161171298000611

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