Definition:Open Ball/Center

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This page is about the center of an open ball. For other uses, see Definition:Center.

Definition

Let $M = \left({A, d}\right)$ be a metric space or pseudometric space.

Let $a \in A$.

Let $B_\epsilon \left({a}\right)$ be the open $\epsilon$-ball of $a$.


In $B_\epsilon \left({a}\right)$, the value $a$ is referred to as the center of the open $\epsilon$-ball.


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.