Definition:Sphere/Metric Space

Definition
Let $M = \struct{A, d}$ be a metric space or pseudometric space.

Let $a \in A$.

Let $\epsilon \in \R_{>0}$ be a strictly positive real number.

The $\epsilon$-sphere of $a$ in $M$ is defined as:


 * $S_\epsilon \paren{a} = \set {x \in A: \map d {x, a} = \epsilon}$