Geodesic
Network character and tightness of the compact-open topology
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 3, pp. 473-482 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 22A99, 46E10, 54A25, 54C35, 54D20, 54H11
Keywords: compact-open topology; network character; tightness; defect; Lindelöf number 
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     author = {Ball, Richard N. and Hager, Anthony W.},
     title = {Network character and tightness of the compact-open topology},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {473--482},
     year = {2006},
     volume = {47},
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     language = {en},
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Ball, Richard N.; Hager, Anthony W. Network character and tightness of the compact-open topology. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 3, pp. 473-482. http://geodesic.mathdoc.fr/item/CMUC_2006_47_3_a9/