Let $X$ be a normed space and let $A, B \subset X$ be totally bounded subsets.
paragraph
admin
1. For any $\lambda \in \mathbb{R}$, the set $\lambda A = \{\lambda a : a \in A\}$ is totally bounded.
2. The Minkowski sum $A + B = \{a + b : a \in A, \, b \in B\}$ is totally bounded.
3. The convex hull $\operatorname{conv}(A)$ is totally bounded.
4. The closure $\overline{A}$ is totally bounded.