Let $f : [ 0,1 ] \longrightarrow \mathbb { R }$ be a continuous function and $E \subseteq [ 0,1 ]$. Which of the following are true?\\
(A) If $E$ is closed, then $f ( E )$ is closed.\\
(B) If $E$ is open, then $f ( E )$ is open.\\
(C) If $E$ is a countable union of closed sets, then $f ( E )$ is a countable union of closed sets.\\
(D) If $f$ injective and $E$ is a countable intersection of open sets, then $f ( E )$ is a countable intersection of open sets.