P normal cone of a cone metric space, given $\epsilon > 0$, can we choose c interior point of P ($c \gg 0$) s.t $\|c\| < \epsilon/K$

Question

I get this statment from paper "Cone metric spaces and fixed point theorems of contractive mappings Huang Long-Guang, Zhang Xian", i failed to understand why there is a guarantee that we can choose an interior point, given $\epsilon >0$ such that $\|c\|<\epsilon / K$, where $K$ is the normal constant.

Answer 1

On page 1469, it says that it is assumed that $P$ is a cone with non-empty interior. Therefore there is some $c_1$ in the interior $P$. But then $ac_1$ is also in the interior of $P$ for any $a > 0$. Hence setting $c=ac_1$ and choosing $a$ sufficiently small will satisfy the requirements.