Last Updated
：2025/11/28
Heine-Borel theorem
Proper noun
Japanese Meaning
数学解析における定理で、n次元ユークリッド空間内の任意の部分集合がコンパクトであるための必要十分条件として、その集合が閉集合であり、かつ有界であることを示す定理です。
Quizzes for review
(mathematical analysis) A theorem which states that for any subset S of an n-dimensional Euclidean space, S is compact if and only if it is both closed and bounded.
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Heine-Borel theorem
In my analysis class, the professor illustrated the Heine-Borel theorem by showing that the closed interval [0,1] is compact because it is closed and bounded.
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In my analysis class, the professor illustrated the Heine-Borel theorem by showing that the closed interval [0,1] is compact because it is closed and bounded.
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