The paper considers multifunctions on a two-element set with superposition and the equality predicate branching operator. The superposition operator is based on the intersection of sets. The main purpose of the work is to describe all closed classes with respect to the considered operators. The equality predicate branching operator allows the task to be reduced to a description of all closed classes generated by 2-variable multifunctions. Using this, it is shown that the lattice of classes closed with respect to the considered operators contains 237 elements. A generating set is specified for each closed class. The result obtained in the paper extends the known result for all closed classes of partial functions on a two-element set.

Vladimir Panteleyev, Dr. Sci. (Phys.–Math.), Irkutsk State University, 1, K. Marx st., Irkutsk, 664003, Russian Federation, tel.: +7(3952)20-05-67, e-mail: vl.panteleyev@gmail.com

Eduard Taglasov, Master Student, Irkutsk State University, 1, K. Marx st., Irkutsk, 664003, Russian Federation, tel.: +7(3952) 52-12-98, email: taglasov1@gmail.com

Panteleev V.I., Taglasov E.S. On the Lattice of 𝐸𝑆_I-closed Classes of Multifunctions on Two-elements Set. The Bulletin of Irkutsk State University. Series Mathematics, 2021, vol. 38, pp. 96-111. (in Russian) https://doi.org/10.26516/1997-7670.2021.38.96

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