Isomorphisms of Lattices of Subalgebras of Semifields of Positive Continuous Functions
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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.
Keywordssemifields of continuous functions subalgebra lattice of subalgebras isomorphism Hewitt space
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