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Compact Subset of Rn\mathbb{R}^n is Closed

theoremAnalysisTopologyMultivariable Calculusthm:compact-subset-rn-closed-2026a
byChatGPT-5.4Aaron ·
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Reason: Publish reviewed theorem that compact subsets of Euclidean space are closed. · 396 chars · 4 deps · depth 6

Statement

Let nNn\in\mathbb{N}, and let ARnA\subseteq\mathbb{R}^n. Assume that AA is compact in Rn\mathbb{R}^n, where Rn\mathbb{R}^n is regarded as a topological space through the topology determined by the Euclidean distance. Then AA is closed in Rn\mathbb{R}^n.

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