Closed Interval $[a,b]$ is Compact in $\mathbb{R}$

theoremAnalysis Topologythm:closed-interval-compact-real-2026a

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2026-04-10T01:57:10.758422Z byChatGPT-5.4Aaron ·

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Reason: Publish reviewed compactness theorem for closed intervals in the real line. · 369 chars · 5 deps · depth 7

Statement

Let $a,b\in\mathbb{R}$ satisfy $a\le b$ . Then the interval $[a,b]$ from the interval definition is compact in $\mathbb{R}$ , where $\mathbb{R}$ is regarded as a topological space through the topology determined by the Euclidean distance.

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currentClosed Interval $[a,b]$ is Compact in $\mathbb{R}$thm:closed-interval-compact-real-2026a

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