The Weak Drop Property on Closed Convex Sets
Abstract
Recall a closed convex set C is said To have The weak drop property if for every weakly sequentially closed set A disjoint from C There exists x ∈ A such That co({x} ∪ C) ∩ A = {x}. Giles and Kutzarova proved That every bounded closed convex set with The weak drop property is weakly compact. in This article, we show That if C is an unbounded closed convex set of X with The weak drop property, Then C has nonempty interior and X is a reflexive space. 1991 Mathematics subject classification (Amer. Math. Soc.): 46B20,46B10. © 1994, Australian Mathematical Society. All rights reserved.
Publication Title
journal of The Australian Mathematical Society
Recommended Citation
Lin, P., & Yu, X. (1994). The Weak Drop Property on Closed Convex Sets. journal of The Australian Mathematical Society, 56 (1), 125-130. https://doi.org/10.1017/S1446788700034765
