Closed Unit Ball

Last updated Nov 1, 2022

Let $X$ be a Normed Vector Space. The Closed Unit Ball is the Closed Ball of radius $1$ about $0 \in X$. It is denoted $\overline{B(X)}$.

1. Closed Unit Ball is Closed because Closed Ball is Closed.
2. Let $r > 0$ and $x \in X$. Then $\overline{B_{r}(x)} = r \overline{B(X)} + x$. Proof is almost identical to Remark 2 in Open Unit Ball.