The formal ball model for -categories

We generalise the construction of the formal ball model for metric spaces due to A. Edalat and R. Heckmann in order to obtain computational models for separated -categories. We fully describe -categories that are (a)Yoneda complete(b)continuous Yoneda complete via their formal ball models. Our resul...

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Bibliographic Details
Published in:Mathematical structures in computer science 2011-02, Vol.21 (1), p.41-64
Main Authors: KOSTANEK, MATEUSZ, WASZKIEWICZ, PAWEŁ
Format: Article
Language:English
Subjects:
Approximation
Ball models
Computation
Computational mathematics
Computer simulation
Construction
Mathematical analysis
Mathematical models
Metric space
Theory
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Summary:We generalise the construction of the formal ball model for metric spaces due to A. Edalat and R. Heckmann in order to obtain computational models for separated -categories. We fully describe -categories that are (a)Yoneda complete(b)continuous Yoneda complete via their formal ball models. Our results yield solutions to two open problems in the theory of quasi-metric spaces by showing that: (a)a quasi-metric space X is Yoneda complete if and only if its formal ball model is a dcpo, and(b)a quasi-metric space X is continuous and Yoneda complete if and only if its formal ball model BX is a domain that admits a simple characterisation of approximation.
ISSN:0960-1295
1469-8072
DOI:10.1017/S0960129510000447