Closure Systems and their
نویسندگان
چکیده
Closure is a fundamental property of many discrete systems. Transitive closure in relations has been well studied, e.g. 1,14,6,5], as has geometric closure 8,9] and closure in various kinds of graphs 17,10]. The closed sets of a closure operator illustrate a kind of well-behaved internal structure that is the main theme of this paper. In Section 1, we examine antimatroid closure spaces. In Section 2, we consider a closure operator that has been widely used in digital image processing 25]. This operator, which can be equally well deened on graphs, is not antimatroid; but it is shown in Section 3 that it retains many of the same structural properties, and is closely related to the classic graph-theoretic theme of domination. Finally, in Section 4, we relate these concepts to premise systemm30].
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