Definition:Open Ball/Normed Division Ring/Radius
< Definition:Open Ball | Normed Division Ring(Redirected from Definition:Radius of Open Ball of Normed Division Ring)
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Definition
Let $\struct {R, \norm{\,\cdot\,} }$ be a normed division ring.
Let $a \in R$.
Let $\epsilon \in \R_{>0}$ be a strictly positive real number.
Let $\map {B_\epsilon} a$ be the open $\epsilon$-ball of $a$.
In $\map {B_\epsilon} a$, the value $\epsilon$ is referred to as the radius of the open $\epsilon$-ball.
Linguistic Note
The plural of radius is radii, pronounced ray-dee-eye.
This irregular plural form stems from the Latin origin of the word radius, meaning ray.
The ugly incorrect form radiuses can apparently be found, but rarely in a mathematical context.
Sources
- 1997: Fernando Q. Gouvea: p-adic Numbers: An Introduction: $\S 2.3$ Topology, Proposition 2.3.5