Solution (source code)

= Solution

\b[True], and the closedness assumption on $Y$ is unnecessary. The <Minkowski sum> has the representation
$$
X+Y=\bigcup_{y\in Y}(X+y).
$$
Each translate of the open set $X$ is open, and an arbitrary union of open sets is open. If $Y$ is empty the union is empty, which is also open.