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BSU bulletin. Mathematics, Informatics

Bibliographic description:
Panteleev V. I.
,
Ryabets L. V.
ON ONE AGGREGATE OF E-CLOSED CLASSES OF HYPERFUNCTIONS OF K RANK // BSU bulletin. Mathematics, Informatics. - 2018. №3. . - С. 14-21.
Title:
ON ONE AGGREGATE OF E-CLOSED CLASSES OF HYPERFUNCTIONS OF K RANK
Financing:
Codes:
DOI: 10.18101/2304-5728-2018-3-14-21UDK: 519.1
Annotation:
Hyperfunctions represent functions defined on a finite set and taking as their values all nonempty subsets of the considered set. In the theory of discrete functions the is- sue of classification is interesting and important concerning different closure opera- tors. One such operator is the closure operator with branching by the equality predicate (E-operator). Such operator belongs to a category of strong closure operators.
The article considers the aggregate of the hyperfunctions of the K rank that preserve permutations on a k-element set. It is shown that these classes are E- closed. In case the permutation splits into cycles of the same simple length, then such classes are E-precomplete. Besides, it is shown that a set containing all function-constants and a function that returns on all sets some fixed non-empty subset of the original set is E-complete.
Keywords:
closure; equality predicate; hyperfunction; closed set; superposition; precomplete set; clon.
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