Definition:Sphere/Metric Space/Center

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

Let $a \in A$.

Let $S_\epsilon \paren{a}$ be the $\epsilon$-sphere of $a$.

In $S_\epsilon \paren{a}$, the value $a$ is referred to as the center of the $\epsilon$-sphere.

Linguistic Note

The British English spelling of center is centre.

The convention on $\mathsf{Pr} \infty \mathsf{fWiki}$ is to use the American English spelling center, but it is appreciated that there may be lapses.


This article incorporates material from sphere (metric space) on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.