# Maximal smooth atlas of an open subset $U$ of a smooth manifold $M$

Let $$M$$ be a smooth $$n$$-dimensional manifold, with smooth maximal atlas $$\mathcal{A}:=\{\varphi:O_a \rightarrow \varphi(O_a)| a \in A\}$$. If I take an open subset $$U \subset M$$, and endow it with the smooth atlas $$\mathcal{A}_U:=\{ \varphi_{U\cap O_a}:U\cap O_a \rightarrow \varphi(U \cap O_a) | a \in A\},$$ is $$\mathcal{A}_U$$ then also a maximal smooth atlas for $$U$$ ?