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Filter-Base (フィルター基・底) (Definition II.2.1)

  • Filter-Base (フィルター基・底) (Definition II.2.1) #Card
    • A subfamily $\mathcal{B}$ of a proper filter $\mathcal{F}$ is a base of $\mathcal{F}$ if for each $F \in \mathcal{F}$, there exists $B \in \mathcal{B}$ such that $B \subset F$. We say $\mathcal{B}$ generates $\mathcal{F}$, denoted $\mathcal{B}^\uparrow = \mathcal{F}$.

Back

Section titled “Back”

A subfamily $\mathcal{B}$ of a proper filter $\mathcal{F}$ is a base of $\mathcal{F}$ if for each $F \in \mathcal{F}$, there exists $B \in \mathcal{B}$ such that $B \subset F$. We say $\mathcal{B}$ generates $\mathcal{F}$, denoted $\mathcal{B}^\uparrow = \mathcal{F}$.

Lean

Section titled “Lean”

Filter.IsBasis / Filter.HasBasis