Notation of all intervals on $\mathbb{R}$

Question

Is there any concise way how to define/denote the set of all intervals on $\mathbb{R}$.

Answer 1

You could use $\left\{\left[a,b\right)|a,b\in\Bbb R\right\}$ or perhaps you could write in terms of the function $f:\Bbb R^2\to\mathcal P(\Bbb R)$ that maps the pair $(a,b)$ to the interval $[a,b)$.