Definition:Open Set/Real Analysis/Real Euclidean Space

Definition
Let $n \ge 1$ be a natural number.

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

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

where $\map B {x, R}$ denotes the open ball of radius $R$ centered at $x$.

Also see

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