Definition open set Let $(X,Y)$ be topological space. A subset $U \subset X$ is called an open set of $X$ if $ U \in Y$
Product topology Let $(X,Y)$ be topological space. The product topology on $X \times Y$ is the topology generated by the basis $\mathcal B$.
$\mathcal B=$ the collection of all sets $U \times V$where $U$ is open in $X$ and $V$ is open in $Y$
Let $X,Y$ be two topological spaces
If $C \subset X$ and $D \subset Y$ are open in $X$ and $Y$, respectively, is $C \times D$ an open set of the product space $X \times Y$ ?