Isomorphisms of Lattices of Subalgebras of Semifields of Positive Continuous Functions

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...

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Bibliographic Details
Published in:Siberian mathematical journal 2019-05, Vol.60 (3), p.526-541
Main Author: Sidorov, V. V.
Format: Article
Language:English
Subjects:
Continuity (mathematics)
Isomorphism
Lattices (mathematics)
Mathematics
Mathematics and Statistics
Unity
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Summary: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.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446619030157