
Journal of Convex Analysis 25 (2018), No. 3, 10451058 Copyright Heldermann Verlag 2018 Dentable Point and BallCovering Property in Banach Spaces Shaoqiang Shang Dept. of Mathematics, Northeast Forestry University, Harbin 150040, P. R. China sqshang@163.com Yunan Cui Dept. of Mathematics, Harbin University of Science and Technology, Harbin 150080, P. R. China cuiya@hrbust.edu.cn [Abstractpdf] We prove that if every bounded subset of $X^{*}$ is $w^{*}$separable, $X$ is compactly locally uniformly convex, $X$ is 2strictly convex and $X$ is nonsquare, then there exists a sequence $\{x_n\}_{n = 1}^\infty $ of dentable points of $B(X)$ such that $S(X) \subset \mathop \cup _{n = 1}^\infty B(x_n,{r_n})$, where $r_{n}< 1$ for all $n\in N$. Moreover, we also prove that if $A$ is a bounded closed convex subset of $X$, then $x\in A$ is a strongly exposed point of $A$ if and only if $x$ is a dentable point of $A$ and $x$ is a $w^{*}$exposed point of $\overline {{A^{{w^*}}}}$. Keywords: Compactly locally uniformly convex, ballcovering property, dentable point, nonsquare space, 2strictly convex space. MSC: 46B20 [ Fulltextpdf (120 KB)] for subscribers only. 