Sphere

Last updated Nov 1, 2022

Let $(M, d)$ be a Metric Space. The Sphere about $x \in M$ of radius $\epsilon > 0$ is $$S_{\epsilon}(x) := {x’ \in X : d(x, x’) = \epsilon}$$

1. $S_\epsilon(x) = \overline{B_{\epsilon}(x)} \setminus B_{\epsilon}(x)$.