Definition:Closed Ball/Metric Space/Center
< Definition:Closed Ball | Metric Space(Redirected from Definition:Center of Closed Ball)
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This page is about Center in the context of Closed Ball of Metric Space. For other uses, see Center.
Definition
Let $M = \struct {A, d}$ be a metric space or pseudometric space.
Let $a \in A$.
Let $\map {B^-_\epsilon} a$ be the closed $\epsilon$-ball of $a$.
In $\map {B^-_\epsilon} a$, the value $a$ is referred to as the center of the closed $\epsilon$-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.