Lattices of Subalgebras of Semirings of Continuous Nonnegative Functions with the Max-Plus

Аннотация

Isomorphisms φ of semirings C^∨(X) of continuous nonnegative functions over an arbitrary Hewitt space X with the condition φ(ℝ⁺) = ℝ⁺ are characterized in this work. It is proved that any isomorphism of lattices of all subalgebras of semirings C^∨ (X) and C^∨ (Y) is induced by a unique isomorphism of semirings excepting the case of one- and two-point Tychonovization of spaces.