Last Updated：2025/12/03

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(topology) A theorem which (in one of its simplest forms) states that a continuous function from an n-dimensional unit cube (in ℝⁿ) to itself has a fixed point.

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Brouwer fixed-point theorem

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Source Word

Brouwer fixed-point theorem

Proper noun

(topology) A theorem which (in one of its simplest forms) states that a continuous function from an n-dimensional unit cube (in ℝⁿ) to itself has a fixed point.

Japanese Meaning

ブロウワーの不動点定理：位相数学における定理で、n次元の単位立方体（ℝⁿ内）からその立方体自身への連続写像は必ず固定点、すなわち写像によって動かされない一点を持つことを示すもの

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During the seminar, the professor used a simple two-dimensional illustration to explain the Brouwer fixed-point theorem, which states that any continuous map from an n-dimensional unit cube to itself has a fixed point.

Google Translation / DeepL Translation

セミナーでは、教授が単純な2次元の図を用いて、n次元の単位立方体から自身への連続写像が必ず不動点を持つと述べる位相幾何学の定理（ブロウワーの不動点定理）を説明した。

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(topology) A theorem which (in one of its simplest forms) states that a continuous function from an n-dimensional unit cube (in ℝⁿ) to itself has a fixed point.

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Brouwer fixed-point theorem

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Brouwer fixed-point theorem

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