Comptes Rendus
no. 10
Mathematical analysis/Functional analysis
Completeness on locally convex cones
the Editorial Board
Mohammad Reza Motallebi1
1Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, Ardabil, P.O. Box 179, Iran
Comptes Rendus. Mathématique, Volume 352 (2014) no. 10, pp. 785-789
is referenced by Corrigendum to the note “Completeness on locally convex cones” [C. R. Acad. Sci. Paris, Ser. I 352 (10) (2014) 785–789]

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2014.09.005

Mohammad Reza Motallebi  1

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