Dentable Point and Ball-Covering Property in Banach Spaces

We prove that if every bounded subset of

is

w^{*} w ∗

-separable,

X X

is compactly locally uniformly convex,

X X

is 2-strictly convex and

X X

is nonsquare, then there exists a sequence

\{x_n\}_{n = 1}^\infty { x n } n = 1 ∞

of dentable points of

B(X) B ( X )

such that

S(X) \subset \mathop \cup _{n = 1}^\infty B(x_n,{r_n}) S ( X ) ⊂ ∪ n = 1 ∞ B ( x n , r n )

, where

r_{n}< 1 r n < 1

for all

n\in N n ∈ N

. Moreover, we also prove that if

A A

is a bounded closed convex subset of

X X

, then

x\in A x ∈ A

is a strongly exposed point of

A A

if and only if

x x

is a dentable point of

A A

and

x x

is a

w^{*} w ∗

-exposed point of

\overline {{A^{{w^*}}}} A w ∗ ‾

.