Compact metric information systems
We present information systems for compact metric spaces using the notions of diameter and strong inclusion of open sets. It is shown that the category of compact metric information systems and metric approximable mappings, dual to the category of compact metric spaces and non-expansive maps, is a partially complete I-category in which canonical solution of domain equations can be found by taking the union (least upper bound) of certain Cauchy chains. For the class of contracting functors, the domain equation has a unique solution. We present such a class which includes the product, the co-product and the hyperspace functor (with Hausdorff metric).
Keywordsmetric information systems strong inclusion Stone duality I-category domain equations Cauchy chains contracting functors unique fixed point
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