Filter Decomposition Theorem (Theorem II.4.1)
QUESTION
Filter Decomposition Theorem (Theorem II.4.1)
Click to reveal answer ANSWER
Every filter $\mathcal{F}$ on $X$ can be uniquely decomposed as:
$$\mathcal{F} = \mathcal{F}^* \wedge \mathcal{F}^\bullet$$
where $\mathcal{F}^*$ is free, $\mathcal{F}^\bullet = (\operatorname{ker} \mathcal{F})^\uparrow$ is principal, and $\mathcal{F}^* \vee \mathcal{F}^\bullet = 2^X$.
Click to see question - ソースノート: chapter2.md
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