Prove that a subset of meager set is also meager I have to prove that a subset $A \subset F$ of meager set $F$ is also a meager set.
From the definition of meager set $F = \bigcup_{n=1}^{\infty}F_n$, where $F_n$ is a nowhere dense set.
As I know we have to show that $A$ has also similiar form, but the question is how do we find these nowhere dense sets, that sum to the whole $A$?

Notice that
$A=F\cap A=\bigcup_{n=1}^\infty F_n\cap A$.
Is $A_n:=F_n\cap A$ a nowhere dense set?
