We consider subsets of $\mathbb R$.
We know the following:
- If $A$ is meagre then $\mathbb R \setminus A$ is not meagre. (Converse not true.)
- If $A$ is meagre then $\mathbb R \setminus A$ is dense. (Converse not true.)
My question: Is is true that if $\mathbb R \setminus A$ is not meagre and $\mathbb R \setminus A$ is dense, then $A$ is meagre ? My intuition says not.