Topology on Classifications in Abstract Design Theory
نویسندگان
چکیده
Abstract Design Theory is a mathematical theory of design based on Yoshikawa’s General Design Theory and Barwise and Seligman’s Channel Theory. Classifications is the structures of Channel theory, and they are used in Abstract Design Theory in order to formulate a scheme of design. Yoshikawa discussed design in terms of topology in General Design Theory. The aim of this paper is to show properties of topological spaces defined by classifications. For a classification A, we shall define a topological space top(A) and a uniform space unif(A) from A. A topological space with the form top(A) is called a classification space, and we shall show that any classification space is uniformizable. Then, we shall discuss about filters on top(A) and show a mathematical interpretation of Yoshikawa’s assertion that the design specification is a filter. Furthermore, we shall argue that the compactness of A, the compactness of top(A), and the completeness of unif(A) are equivalent.Design Theory is a mathematical theory of design based on Yoshikawa’s General Design Theory and Barwise and Seligman’s Channel Theory. Classifications is the structures of Channel theory, and they are used in Abstract Design Theory in order to formulate a scheme of design. Yoshikawa discussed design in terms of topology in General Design Theory. The aim of this paper is to show properties of topological spaces defined by classifications. For a classification A, we shall define a topological space top(A) and a uniform space unif(A) from A. A topological space with the form top(A) is called a classification space, and we shall show that any classification space is uniformizable. Then, we shall discuss about filters on top(A) and show a mathematical interpretation of Yoshikawa’s assertion that the design specification is a filter. Furthermore, we shall argue that the compactness of A, the compactness of top(A), and the completeness of unif(A) are equivalent.
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