ISOMORPHISMS OF LATTICES OF SUBALGEBRAS OF SEMIRINGS OF CONTINUOUS NONNEGATIVE FUNCTIONS

摘要

In this work, lattice isomorphisms of semirings C~+(X) of continuous nonnegative functions over an arbitrary topological space X are characterized. It is proved that any isomorphism of lattices of all subalgebras with a unit of semirings C~+(X) and C~+(Y) is induced by a unique isomorphism of semirings. The same result is also correct for lattices of all subalgebras excepting the case of two-point Tychonovization of spaces.