Order (包含関係による順序)
QUESTION
Order (包含関係による順序)
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Ordered by inclusion $\subset$. The set of all filters on $X$ ordered by inclusion is a complete lattice.
- **Infimum (交わり)**: $\mathcal{F}_0 \wedge \mathcal{F}_1 = \mathcal{F}_0 \cap \mathcal{F}_1$
- **Supremum (結び)**: $\mathcal{F}_0 \vee \mathcal{F}_1 = \{F_0 \cap F_1 : F_0 \in \mathcal{F}_0, F_1 \in \mathcal{F}_1\}$ (proper iff $F_0 \cap F_1 \neq \emptyset$ for all $F_0 \in \mathcal{F}_0, F_1 \in \mathcal{F}_1$)
Click to see question - ソースノート: chapter2.md
- カードID: order
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