This paper deals with the locallyβ-convex analysis that generalizes the locally convex analysis. The second separation theorem in locallyβ-convex spaces, the Minkowski theorem and the Krein-Milman theorem in theβ-c...This paper deals with the locallyβ-convex analysis that generalizes the locally convex analysis. The second separation theorem in locallyβ-convex spaces, the Minkowski theorem and the Krein-Milman theorem in theβ-convex analysis are given. Moreover, it is obtained that the U F-boundedness and the U B-boundedness in its conjugate cone are equivalent if and only if X is subcomplete.展开更多
文摘This paper deals with the locallyβ-convex analysis that generalizes the locally convex analysis. The second separation theorem in locallyβ-convex spaces, the Minkowski theorem and the Krein-Milman theorem in theβ-convex analysis are given. Moreover, it is obtained that the U F-boundedness and the U B-boundedness in its conjugate cone are equivalent if and only if X is subcomplete.
