| Title:
|
On three equivalences concerning Ponomarev-systems (English) |
| Author:
|
Ge, Ying |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
239-246 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\lbrace {\mathcal P}_n\rbrace $ be a sequence of covers of a space $X$ such that $\lbrace st(x,{\mathcal P}_n)\rbrace $ is a network at $x$ in $X$ for each $x\in X$. For each $n\in \mathbb N$, let ${\mathcal P}_n=\lbrace P_{\beta }:\beta \in \Lambda _n\rbrace $ and $\Lambda _ n$ be endowed the discrete topology. Put $M=\lbrace b=(\beta _n)\in \Pi _{n\in \mathbb N}\Lambda _ n: \lbrace P_{\beta _n}\rbrace $ forms a network at some point $x_b\ in \ X\rbrace $ and $f:M\longrightarrow X$ by choosing $f(b)=x_b$ for each $b\in M$. In this paper, we prove that $f$ is a sequentially-quotient (resp. sequence-covering, compact-covering) mapping if and only if each $\mathcal {P}_n$ is a $cs^*$-cover (resp. $fcs$-cover, $cfp$-cover) of $X$. As a consequence of this result, we prove that $f$ is a sequentially-quotient, $s$-mapping if and only if it is a sequence-covering, $s$-mapping, where “$s$” can not be omitted. (English) |
| Keyword:
|
Ponomarev-system |
| Keyword:
|
point-star network |
| Keyword:
|
$cs^*$-(resp. $fcs$- |
| Keyword:
|
$cfp$-)cover |
| Keyword:
|
sequentially-quotient (resp. sequence-covering |
| Keyword:
|
compact-covering) mapping |
| MSC:
|
54E40 |
| idZBL:
|
Zbl 1164.54363 |
| idMR:
|
MR2260382 |
| . |
| Date available:
|
2008-06-06T22:48:13Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108002 |
| . |
| 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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| . |
