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Openai/687e18a6-9c94-8003-9238-502a348ed325
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==== ⋃λ∈Λfλ は B の構成素材(生成元)です。\boxed{ ==== \bigcup_{\lambda \in \Lambda} f_\lambda } \text{ は } \boxed{ \mathcal{B} } \text{ の構成素材(生成元)です。}λ∈Λ⋃fλ は B の構成素材(生成元)です。 * ∪λ fλ は B\mathcal{B}B に含まれます(部分集合): ⋃λ∈Λfλ⊂B\bigcup_{\lambda \in \Lambda} f_\lambda \subset \mathcal{B}λ∈Λ⋃fλ⊂B ただし右辺の B\mathcal{B}B の要素は、左辺の集合を有限個交差して作ったものも含みます。 * B\mathcal{B}B のすべての要素は、∪λ fλ の要素を有限個交差したものでできています。 ==== <syntaxhighlight> ∪λ fλ (1次元的に制限された集合たち) ==== │ │(有限個交差) ↓ 𝔅 = { ⋂ U_i | U_i ∈ fλ_i } (3次元的に制限された集合も含む) ↓ 開集合系(この𝔅の合併で全部生成できる) </syntaxhighlight>
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