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
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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 
@article{TIMM_2015_21_3_a8,
     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},
     year = {2015},
     volume = {21},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a8/}
}
TY  - JOUR
AU  - E. M. Vechtomov
AU  - V. V. Sidorov
TI  - Definability of Hewitt spaces by the lattices of subalgebras of semifields of continuous positive functions with max-plus
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2015
SP  - 78
EP  - 88
VL  - 21
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a8/
LA  - ru
ID  - TIMM_2015_21_3_a8
ER  - 
%0 Journal Article
%A E. M. Vechtomov
%A V. V. Sidorov
%T Definability of Hewitt spaces by the lattices of subalgebras of semifields of continuous positive functions with max-plus
%J Trudy Instituta matematiki i mehaniki
%D 2015
%P 78-88
%V 21
%N 3
%U http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a8/
%G ru
%F TIMM_2015_21_3_a8
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/

[1] Varankina V.I., Vechtomov E.M., Semenova I.A., “Polukoltsa nepreryvnykh neotritsatelnykh funktsii: delimost, idealy, kongruentsii”, Fundament. i prikl. matematika, 4:2 (1998), 493–510 | MR | Zbl

[2] Vechtomov E.M., “Voprosy opredelyaemosti topologicheskikh prostranstv algebraicheskimi sistemami nepreryvnykh funktsii”, Itogi nauki i tekhniki. Ser. Algebra. Topologiya. Geometriya, 28, VINITI, M., 1990, 3–46

[3] Vechtomov E.M., “Koltsa nepreryvnykh funktsii. Algebraicheskie aspekty”, Itogi nauki i tekhniki. Ser. Algebra. Topologiya. Geometriya, 29, VINITI, M., 1991, 119–191 | MR

[4] Vechtomov E.M., “Reshetka podalgebr kolets nepreryvnykh funktsii i khyuittovskie prostranstva”, Mat. zametki, 62:5 (1997), 687–693 | DOI | MR | Zbl

[5] Vechtomov E.M., Sidorov V.V., “Opredelyaemost polukolets nepreryvnykh funktsii reshetkoi ikh podalgebr”, Vestn. Syktyvkar. un-ta. Ser.1: Matematika. Mekhanika. Informatika, 2010, no. 11, 112–125

[6] Vechtomov E.M., Sidorov V.V., “Izomorfizmy reshetok podalgebr polukolets nepreryvnykh neotritsatelnykh funktsii”, Fundament. i prikl. matematika, 16:3 (2010), 63–103 | MR

[7] Vechtomov E.M., Sidorov V.V., Chuprakov D.V., Polukoltsa nepreryvnykh funktsii, Izd-vo VyatGGU, Kirov, 2011, 312 pp.

[8] Gelfand I.M., Kolmogorov A.N., “O koltsakh nepreryvnykh funktsii na topologicheskikh prostranstvakh”, Dokl. AN SSSR, 22:1 (1939), 11–15

[9] Salii V.N., Reshetki s edinstvennymi dopolneniyami, Nauka, M., 1984, 128 pp. | MR

[10] Engelking R., Obschaya topologiya, Mir, M., 1986, 752 pp. | MR

[11] Gillman L., Jerison M., Rings of continuous functions, Springer-Verlag, N.J., 1976, 303 pp. | MR | Zbl

[12] Hewitt E., “Rings of real-valued continuous functions”, Trans. Amer. Math. Soc., 64:1 (1948), 45–99 | DOI | MR | Zbl