i want to know if s_0 is strictly less than 1 in the the given inequality of $t^{-1}x=s_0 $?

Question

Let $A$ be a convex absorbing set in the vector space $X$.

The sets $C$ and $B$ are defined as follows:

$C= \{ x : \mu_A(x) \leq1\}$ and $B=\{x: \mu_A(x) < 1\}$. this also means that $B\subset A \subset C$

let $\mu_C(x)<t$ for some t. This means that $\mu_C(t^{-1} x)<1$. So there exists some $s_0$ such that $t^{-1}x=s_0 c$ where $c \in C$

Here is $s_0<1$ or $s_0 \leq 1$???