Definition:Open Set/Real Analysis/Real Euclidean Space

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Definition

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

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


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

$\forall x \in U : \exists R > 0: \map B {x, R} \subset U$

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


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