| Title:
|
Spaces with countable $sn$-networks (English) |
| Author:
|
Ying, Ge |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
169-176 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we prove that a space $X$ is a sequentially-quotient $\pi$-image of a metric space if and only if $X$ has a point-star $sn$-network consisting of $cs^*$-covers. By this result, we prove that a space $X$ is a sequentially-quotient $\pi$-image of a separable metric space if and only if $X$ has a countable $sn$-network, if and only if $X$ is a sequentially-quotient compact image of a separable metric space; this answers a question raised by Shou Lin affirmatively. We also obtain some results on spaces with countable $sn$-networks. (English) |
| Keyword:
|
separable metric space |
| Keyword:
|
sequentially-quotient ($\pi$ |
| Keyword:
|
compact) mapping |
| Keyword:
|
point-star $sn$-network |
| Keyword:
|
$cs*$-cover |
| MSC:
|
54C05 |
| MSC:
|
54C10 |
| MSC:
|
54D65 |
| MSC:
|
54E40 |
| idZBL:
|
Zbl 1098.54025 |
| idMR:
|
MR2076868 |
| . |
| Date available:
|
2009-05-05T16:44:06Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119445 |
| . |
| Reference:
|
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| . |
