Geodesic
$E$-closed sets of hyperfunctions on two-element set
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 2, pp. 231-241

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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
Mots-clés : composition. 
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     author = {Vladimir I. Panteleyev and Leonid V. Riabets},
     title = {$E$-closed sets of hyperfunctions on two-element set},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {231--241},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_2_a9/}
}
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Vladimir I. Panteleyev; Leonid V. Riabets. $E$-closed sets of hyperfunctions on two-element set. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 2, pp. 231-241. http://geodesic.mathdoc.fr/item/JSFU_2020_13_2_a9/