A general view of approximation (Q2432576)

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 \textit{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.