Definition:Open Set/Real Analysis/Real Euclidean Space

Definition
Let $n\geq1$ be a natural number.

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

Then $U$ is open (in $\R^n$) :
 * $\forall x\in U : \exists R>0 : B(x, R) \subset U$

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

Also see

 * Definition:Closed Subset of Real Euclidean Space
 * Definition:Neighborhood in Real Euclidean Space