Banach Spaces That Admit Support Sets
نویسنده
چکیده
It is shown that the existence of a closed convex set all of whose points are properly supported in a Banach space is equivalent to the existence of a certain type of uncountable ordered one-sided biorthogonal system. Under the continuum hypothesis, we deduce that this notion is weaker than the existence of an uncountable biorthogonal system. Introduction. We will say a closed convex set C in a Banach space X is a support set if for every z 2 C, there is a 2 X such that (z) = inf
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