On one aggregate of е-closed classes of hyperfunctions of к rank

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 issue of classification is interesting and important concerning different closure operators. 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 К 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.