FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 3, PAGES 63-103

Isomorphisms of lattices of subalgebras of semirings of continuous nonnegative functions

E. M. Vechtomov
V. V. Sidorov

Abstract

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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.

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Last modified: March 24, 2011