Countable Character (可算指標の収束) (Definition III.2.6)

• Countable Character (可算指標の収束) (Definition III.2.6) #Card
  • A convergence $\xi$ is of countable character at $x$ if there exists a pavement of $\xi$ at $x$ consisting of countably based filters; of countable character if so at each point.

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A convergence $\xi$ on $X$ is said to be of countable character at $x \in X$ if there exists a pavement of $\xi$ at $x$ consisting of countably based filters. A convergence is called of countable character if it is of countable character at each point.

• $\iota$, $o$ は有限指標；$\nu_\mathbb{R}$, $\sigma_\mathbb{R}$ は可算指標。
• 非可算集合上の prime cofinite convergence $\pi[x_\infty, (X)_0]$ は可算指標でない（Proposition II.2.19 による）。

Lean

位相・前位相の場合は第一可算性 FirstCountableTopology X に対応