Unit Sphere

Last updated Nov 1, 2022

Let $X$ be a Normed Vector Space. The Unit Sphere is the Sphere of radius $1$ about $0 \in X$. It is denoted $S(X)$.

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