Geodesic
Definability of Hewitt spaces by the lattices of subalgebras of semifields of continuous positive functions with max-plus
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 78-88

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The lattice $\mathbb{A}(U^{\vee}(X))$ of subalgebras of the semifield $U^{\vee}(X)$ of all 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 $\mathbb{R}$. The main result of the paper is the proof of the fact that any Hewitt space $X$ is determined by the lattice $\mathbb{A}(U^{\vee}(X))$.
Keywords: semifield of continuous functions, lattice of subalgebras, hewitt space, max-addition.
Mots-clés : subalgebra, isomorphism 
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     author = {E. M. Vechtomov and V. V. Sidorov},
     title = {Definability of {Hewitt} spaces by the lattices of subalgebras of semifields of continuous positive functions with max-plus},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {78--88},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a8/}
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E. M. Vechtomov; V. V. Sidorov. Definability of Hewitt spaces by the lattices of subalgebras of semifields of continuous positive functions with max-plus. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 78-88. http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a8/