| Title:
|
$\Sigma_s$-products revisited (English) |
| Author:
|
Rojas-Hernández, Reynaldo |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
243-255 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that any $\Sigma_s$-product of at most $\mathfrak{c}$-many $L\Sigma(\leq \omega)$-spaces has the $L\Sigma(\leq \omega)$-property. This result generalizes some known results about $L\Sigma(\leq \omega)$-spaces. On the other hand, we prove that every $\Sigma_s$-product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every $\Sigma_s$-product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [{Lifting the Collins-Roscoe property by condensations}, Topology Proc. {42} (2012), 1--15]. Besides, we prove that if $X$ is a simple Lindelöf $\Sigma$-space, then $C_p(X)$ has the Collins-Roscoe property. (English) |
| Keyword:
|
$\Sigma_s$-product |
| Keyword:
|
Lindelöf $\Sigma$-space |
| Keyword:
|
$L\Sigma(\leq \omega)$-space |
| Keyword:
|
monotonically monolithic space |
| Keyword:
|
Collins-Roscoe space |
| Keyword:
|
function space |
| Keyword:
|
simple space |
| MSC:
|
54B10 |
| MSC:
|
54C35 |
| MSC:
|
54D99 |
| idZBL:
|
Zbl 06433822 |
| idMR:
|
MR3338737 |
| DOI:
|
10.14712/1213-7243.2015.122 |
| . |
| Date available:
|
2015-04-25T17:09:17Z |
| Last updated:
|
2017-08-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144245 |
| . |
| 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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| 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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| 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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| . |
