This article is cited in 1 scientific paper (total in 1 paper)
$E$-closed sets of hyperfunctions on two-element set
Vladimir I. Panteleyev, Leonid V. Riabets
Irkutsk State University, Irkutsk, Russian Federation
Hyperfunctions are functions that are defined on a finite set and return all non-empty subsets of the considered set as their values. This paper deals with the classification of hyperfunctions on a two-element set. We consider the composition and the closure operator with the equality predicate branching ($E$-operator). $E$-closed sets of hyperfunctions are sets that are obtained using the operations of adding dummy variables, identifying variables, composition, and $E$-operator. It is shown that the considered classification leads to a finite set of closed classes. The paper presents all 78 $E$-closed classes of hyperfunctions, among which there are 28 pairs of dual classes and 22 self-dual classes. The inclusion diagram of the $E$-closed classes is constructed, and for each class its generating system is obtained.
closure, equality predicate, hyperfunction, closed set, composition.
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Received in revised form: 06.01.2020
Vladimir I. Panteleyev, Leonid V. Riabets, “$E$-closed sets of hyperfunctions on two-element set”, J. Sib. Fed. Univ. Math. Phys., 13:2 (2020), 231–241
Citation in format AMSBIB
\by Vladimir~I.~Panteleyev, Leonid~V.~Riabets
\paper $E$-closed sets of hyperfunctions on two-element set
\jour J. Sib. Fed. Univ. Math. Phys.
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This publication is cited in the following articles:
Panteleev I V., Riabets V L., “Classification of Multioperations of Rank 2 By E-Precomplete Sets”, Bull. Irkutsk State Univ.-Ser. Math., 34 (2020), 93–108
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