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A general view of approximation. (English) Zbl 1113.54013

In this interesting paper, the authors start from the idea of approximating real numbers by decimal expansions to develop a notion of ‘approximation system’, which is a preordered set with top element, equipped with a family of covers which satisfy axioms like those for a nearness. They show that the category of such structures is equivalent (in a weak sense) to the category of information systems in the sense of D. Scott equipped with a similar nearness-like structure (they call these ‘stratified information systems’), and also to the category of complete nearness frames. They also describe how to proceed directly from an approximation system to its ‘space of points’, that is the spectrum of the corresponding nearness frame.

MSC:

54E17 Nearness spaces
06D22 Frames, locales
06F99 Ordered structures
18B30 Categories of topological spaces and continuous mappings (MSC2010)
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