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Closure systems and their structure. (English) Zbl 0993.06004

Summary: Closure is a fundamental property of many discrete systems. Transitive closure in relations has been well studied, as has geometric convexity closure and closure in various kinds of graphs. The closed sets of these uniquely generated, antimatroid operators illustrate a well-behaved internal structure. This paper shows that much of this structure is preserved even by closure operators that are not uniquely generated.

MSC:

06A15 Galois correspondences, closure operators (in relation to ordered sets)
68U10 Computing methodologies for image processing
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