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Centered Family / Filter-Subbase (有心族・準基) (Definition II.2.3)

  • Centered Family / Filter-Subbase (有心族・準基) (Definition II.2.3) #Card
    • A family $\mathcal{D}$ of subsets of $X$ is centered (or has the finite intersection property) if for any finite subfamily $\mathcal{D}0 \subset{\text{fin}} \mathcal{D}$, the intersection $\bigcap_{D \in \mathcal{D}_0} D$ is non-empty.

Back

Section titled “Back”

A family $\mathcal{D}$ of subsets of $X$ is centered (or has the finite intersection property) if for any finite subfamily $\mathcal{D}0 \subset{\text{fin}} \mathcal{D}$, the intersection $\bigcap_{D \in \mathcal{D}_0} D$ is non-empty.

Lean

Section titled “Lean”

有限交叉性 FIP → Filter.generate で生成。Filter.generate