Show:
Let $\{U_{\lambda}: \lambda \in L\}$ be a base of neighbourhoods at $0$ in a topological vector space $\mathcal{X}$. Then $\{U_{\lambda}+ U_{\lambda}: \lambda \in L\}$ is also a base of neighbourhoods.
I have an intuition that this is to proved using the continuity of the "+" operator, but am not able to proceed.