no. 10
Mathematical analysis/Functional analysis
Completeness on locally convex cones
[Intégralité de cônes localement convexes]

Présenté par : the Editorial Board

Motallebi, Mohammad Reza1
1 Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, Ardabil, P.O. Box 179, Iran
Comptes Rendus. Mathématique, Tome 352 (2014) no. 10, pp. 785-789.
est référencé par Corrigendum to the note “Completeness on locally convex cones” [C. R. Acad. Sci. Paris, Ser. I 352 (10) (2014) 785–789]

Nous étudions des sous-ensembles complets et compacts pour le bas, le haut et les topologies symétriques d'un cône localement convexe, et prouvons que les ensembles faiblement fermés sont faiblement compacts à chaque fois qu'ils sont faiblement précompacts. Cela conduit à la faible* compacité des polaires des quartiers et à la faible compacité des quartiers inférieur, supérieur et symétrique.

We investigate complete and compact subsets for the lower, upper and symmetric topologies of a locally convex cone and prove that weakly closed sets will be weakly compact, whenever they are weakly precompact. This leads to the weak* compactness of the polars of neighborhoods and weak compactness of the lower, upper and symmetric neighborhoods.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.09.005
Motallebi, Mohammad Reza 1

1 Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, Ardabil, P.O. Box 179, Iran 
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Motallebi, Mohammad Reza. Completeness on locally convex cones. Comptes Rendus. Mathématique, Tome 352 (2014) no. 10, pp. 785-789. doi : 10.1016/j.crma.2014.09.005. http://www.numdam.org/articles/10.1016/j.crma.2014.09.005/

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