Upgrade to access all content for this subject

Let $L$ be the $\mathbb{R}$-vector space of real valued functions on $\mathbb{R}$.

Which of the following sets has the same cardinality as its dual $L^*$?

$\mathbb{R}$

$\mathbb{Q}$

The set of total orders on $\mathbb{R}$

The set of subsets of the power set of $\mathbb{R}$