Category:Examples of Open Balls
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This category contains examples of Open Ball of Metric Space.
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 open $\epsilon$-ball of $a$ in $M$ is defined as:
- $\map {B_\epsilon} a := \set {x \in A: \map d {x, a} < \epsilon}$
If it is necessary to show the metric or pseudometric itself, then the notation $\map {B_\epsilon} {a; d}$ can be used.
Pages in category "Examples of Open Balls"
The following 2 pages are in this category, out of 2 total.