# Definition:Open Set/Real Analysis/Real Euclidean Space

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## Definition

Let $n\geq1$ be a natural number.

Let $U \subseteq \R^n$ be a subset.

Then $U$ is open (in $\R^n$) if and only if:

$\forall x\in U : \exists R>0 : B(x, R) \subset U$

where $B(x,R)$ is the open ball of radius $R$ centered at $x$.