Does there exist a set $M \subset \mathbb{R}^2$ which has the following two properties:


* Forall $x \in \mathbb{R}$ the set $\{y \in \mathbb{R} \mid (x,y) \in M\}$ is countable.
* Forall $y \in \mathbb{R}$ the set $\{x \in \mathbb{R} \mid (x,y) \notin M\}$ is countable.



Does there exist a subset of $\mathbb{R}^2$ which is "very small" and "very big" in the specified way?
It is a theorem of Sierpinski (Sur un theoreme equivalent a l'hypothese du continu) that the existence of such a set is equivalent to the continuum hypothesis.


