Chu Space
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High Quality Content by WIKIPEDIA articles! Chu spaces generalize the notion of topological space by dropping the requirements that the set of open sets be closed under union and finite intersection, that the open sets be extensional, and that the membership predicate (of points in open sets) be two-valued. The definition of continuous function remains unchanged other than having to be worded carefully to continue to make sense after these generalizations.Understood statically, a Chu space (A, r, X) over a set K consists of a set A of points, a set X of states, and a function r : A × X K. Thi...
High Quality Content by WIKIPEDIA articles! Chu spaces generalize the notion of topological space by dropping the requirements that the set of open sets be closed under union and finite intersection, that the open sets be extensional, and that the membership predicate (of points in open sets) be two-valued. The definition of continuous function remains unchanged other than having to be worded carefully to continue to make sense after these generalizations.Understood statically, a Chu space (A, r, X) over a set K consists of a set A of points, a set X of states, and a function r : A × X K. This makes it an A × X matrix with entries drawn from K, or equivalently a K-valued binary relation between A and X (ordinary binary relations being 2-valued).
