A character on $C\left( \mathbb{R}^n\right)$ (the set of all complex-valued continuous functions on $\mathbb{R}^n$) is a continuous $^*$-algebra homomorphism into $\mathbb{C}$. For any fixed $x_0\in \mathbb{R}^n$, the function $\widetilde{x_0}:C\left( \mathbb{R}^n\right) \rightarrow \mathbb{C}$ defiend by $\widetilde{x_0}(f)=f(x_0)$ is a character.
Are there any characters of $C\left( \mathbb{R}^n\right)$ not of this form?
Thanks much in advance!
EDIT: Just to clarify, a $^*$-algebra homomorphism preserves addition, scalar multiplication, multiplication, the involution, and sends $1$ to $1$.