Abstract
In [1] it was proved that the unit ball of a reflexive Banach space has an uncountable set of extreme points. In this note it is shown that this set is also massive in some topological sense.
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J. Lindenstrauss and R. Phelps, “Extreme point properties of convex bodies in reflexive Banach spaces,” Israel J. Math.,6, 39–48 (1968).
R. Phelps, Lectures on Choquet's Theorem, Van Nostrand, Princeton (1966).
W. B. Johnson and H. P. Rosenthal, “On w*-basic sequences and their applications to the study of Banach spaces,” Studia Math.,43, 77–92 (1972).
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Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 315–320, September, 1976.
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Kadets, M.I., Fonf, V.P. Some properties of the set of extreme points of the unit ball of a Banach space. Mathematical Notes of the Academy of Sciences of the USSR 20, 737–739 (1976). https://doi.org/10.1007/BF01097240
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DOI: https://doi.org/10.1007/BF01097240