2.AdjectiveAdmitting slices of arbitrarily small diameter, where a slice of C is a subset of the form
S
(
λ
,
α
)
{\displaystyle S(\lambda ,\alpha )}
=
{
y
∈
C
|
λ
(
y
)
≥
|
|
λ
|
|
∞
,
C
−
α
}
{\displaystyle \{y\in C\;|\;\lambda (y)\geq ||\lambda ||_{\infty ,C}-\alpha \}}
for some
λ
∈
Y
∗
{\displaystyle \lambda \in Y^{*}}
and some 0}">
α
>
0
{\displaystyle \alpha >0}
0}">.