Abstract
We consider the lattice of subalgebras of a semifield U(X) of positive continuous functions on an arbitrary topological space X and its sublattice of subalgebras with unity. We prove that each isomorphism of the lattices of subalgebras with unity of semifields U(X) and U(Y) is induced by a unique isomorphism of the semifields. The same result holds for lattices of all subalgebras excluding the case of the double-point Tychonoff extension of spaces.
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Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 3, pp. 676–694.
The author was supported by the State Task of the Ministry of Education and Science (Grant 1.5879.2017/8.9).
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Sidorov, V.V. Isomorphisms of Lattices of Subalgebras of Semifields of Positive Continuous Functions. Sib Math J 60, 526–541 (2019). https://doi.org/10.1134/S0037446619030157
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DOI: https://doi.org/10.1134/S0037446619030157