Definition:Closed Set/Real Analysis
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This page is about Closed Set in the context of Real Analysis. For other uses, see Closed.
Definition
Real Numbers
Let $S \subseteq \R$ be a subset of the set of real numbers.
Then $S$ is closed (in $\R$) if and only if its complement $\R \setminus S$ is an open set.
Real Euclidean Space
Let $n \ge 1$ be a natural number.
Let $S \subseteq \R^n$ be a subset.
Then $S$ is closed (in $\R^n$) if and only if its complement $\R^n \setminus S$ is an open set.
Also see
- Results about closed sets can be found here.