Separation of Convex Sets in Linear Topological Spaces
نویسنده
چکیده
This paper discusses under what conditions two disjoint convex subsets of a linear topological space can be separated by a continuous linear functional. The equivalence of several forms of the Hahn-Banach theorem is proven. The separation problem is considered in linear topological spaces, locally convex linear topological spaces, Banach spaces, and finally finite dimensional Banach spaces. A number of examples are included to show the necessity of the hypotheses of various theorems.
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