Banach spaces that admit support sets
Jonathan Michael Borwein, Jon D. Vanderwerff · Proceedings of the American Mathematical Society · 1996
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.