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.
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Mohammad Reza Motallebi 1
@article{CRMATH_2014__352_10_785_0, author = {Mohammad Reza Motallebi}, title = {Completeness on locally convex cones}, journal = {Comptes Rendus. Math\'ematique}, pages = {785--789}, publisher = {Elsevier}, volume = {352}, number = {10}, year = {2014}, doi = {10.1016/j.crma.2014.09.005}, language = {en}, }
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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.005/
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