How to interpret domain of a function where the input is scalar to the power vector.

Question

From the paper that introduced PointNet(Qi et al,2016).

We have:

$f(\{x_1,...,x_n\}) \approx g(h(x_1),...,h(x_n)),$

where $f: 2^{\mathbb{R}^N} \rightarrow \mathbb{R}^N$, and $h: \mathbb{R}^N \rightarrow \mathbb{R}^K$ is symmetirc function.

My question is:

what does $2^{\mathbb{R}^N} \rightarrow \mathbb{R}^N$ exactly mean? I am confused about $2^{\mathbb{R}^N}$. I am aware of the fact it is a set of cardinality two to the power vector of real numbers of dimension N.