| Title:
|
Network character and tightness of the compact-open topology (English) |
| Author:
|
Ball, Richard N. |
| Author:
|
Hager, Anthony W. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
473-482 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
compact-open topology |
| Keyword:
|
network character |
| Keyword:
|
tightness |
| Keyword:
|
defect |
| Keyword:
|
Lindelöf number |
| MSC:
|
22A99 |
| MSC:
|
46E10 |
| MSC:
|
54A25 |
| MSC:
|
54C35 |
| MSC:
|
54D20 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 1150.54016 |
| idMR:
|
MR2281009 |
| . |
| Date available:
|
2009-05-05T16:58:49Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119608 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
