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Keywords:
compact-open topology; network character; tightness; defect; Lindelöf number
compact-open topology; network character; tightness; defect; Lindelöf number
Summary:
For Tychonof\text{}f $X$ and $\alpha$ an infinite cardinal, let $\alpha \operatorname{def} X := $ the minimum number of $\alpha $\,cozero-sets of the Čech-Stone compactification which intersect to $X$ (generalizing $\Bbb R$-defect), and let $\operatorname{rt} X := \min _\alpha \max (\alpha , \alpha \operatorname{def} X)$. Give $C(X)$ the compact-open topology. It is shown that $\tau C(X)\leq n\chi C(X) \leq \operatorname{rt}X=\max (L(X),L(X) \operatorname{def} X)$, where: $\tau$ is tightness; $n\chi$ is the network character; $L(X)$ is the Lindel"{o}f number. For example, it follows that, for $X$ Čech-complete, $\tau C(X)=L(X)$. The (apparently new) cardinal functions $n\chi C$ and $\operatorname{rt}$ are compared with several others.
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