Abstract
Square Banach spaces are characterized among real Banach spaces in terms of the Alfsen-Effros structure topology on the extreme points of the dual ball. As a corollary, one has that the class of separable square spaces coincides with the class of separableG-spaces. It is also shown that for aG-space (hence for a square space) regularity of the quotient structure topology is equivalent to complete regularity, and that square spaces exist for which this topology is not regular.
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