Filter-Base (フィルター基・底) (Definition II.2.1)
QUESTION
Filter-Base (フィルター基・底) (Definition II.2.1)
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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 $\mathcal{B}^\uparrow = \mathcal{F}$.
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