What does $1_{\mathbb{R}}$ mean?

Question

Please help. I can't understand the prove if I don't know what does $1_{\mathbb{R}}$ mean. Here is the example :

For $a\in\mathbb{R}$, $|a|<1$ apply the Banach theorem to show that functional equation $f(x)=x+a\sin f(x)$ has unique solution $f\in C([0,1])$. Proof: Using uniform norm we have $F(h)=1_{\mathbb{R}}+a\sin h$, $F\in C([0,1])$. $d(F(h_1),F(h_2))=||F(h_1)-F(h_2)||...$

Answer 1

Here

$$\begin{align} 1_{\Bbb R}:\Bbb R & \to \Bbb R, \\ r & \mapsto r \end{align}$$

is the identity function on $\Bbb R$.