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 J. Sib. Fed. Univ. Math. Phys., 2020, Volume 13, Issue 2, Pages 231–241 (Mi jsfu834)

$E$-closed sets of hyperfunctions on two-element set

Vladimir I. Panteleyev, Leonid V. Riabets

Irkutsk State University, Irkutsk, Russian Federation

Abstract: 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.

Keywords: closure, equality predicate, hyperfunction, closed set, composition.

DOI: https://doi.org/10.17516/1997-1397-2020-13-2-231-241

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UDC: 519.716
Accepted: 13.02.2020
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Citation: 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
\Bibitem{PanRya20} \by Vladimir~I.~Panteleyev, Leonid~V.~Riabets \paper $E$-closed sets of hyperfunctions on two-element set \jour J. Sib. Fed. Univ. Math. Phys. \yr 2020 \vol 13 \issue 2 \pages 231--241 \mathnet{http://mi.mathnet.ru/jsfu834} \crossref{https://doi.org/10.17516/1997-1397-2020-13-2-231-241} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000526181200010} 

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This publication is cited in the following articles:
1. 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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