Determinability of Hewitt spaces by the lattices of subalgebras with unit of semifields of continuous positive functions with max-plus

Abstract

The lattice A₁(U^∨(X)) of subalgebras with unit of the semifield U^∨(X) of continuous positive functions defined on a topological space X is considered. A topological space is said to be a Hewitt space if it is homeomorphic to a closed subspace of a Tychonoff power of the real line R. The main achievement of the paper is the proof of the fact that any Hewitt space X is determined by the lattice A₁(U^∨(X)).