List of top Functional Analysis Questions on Normed Linear Spaces: Open, Closed, Convex and Connected Sets

Let \(E_1\) and \(E_2\) be subsets of a normed linear space \(X\), and
\[ E_1 + E_2 = \{x+y : x \in E_1,\ y \in E_2\} \] \[ E_1 \times E_2 = \{(x,y) : x \in E_1,\ y \in E_2\}. \] Which one of the following is NOT TRUE?