| Title:
|
Compact images of spaces with a weaker metric topology (English) |
| Author:
|
Yan, Peng-fei |
| Author:
|
Lü, Cheng |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
921-926 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
If $X$ is a space that can be mapped onto a metric space by a one-to-one mapping, then $X$ is said to have a weaker metric topology. \endgraf In this paper, we give characterizations of sequence-covering compact images and sequentially-quotient compact images of spaces with a weaker metric topology. The main results are that \endgraf (1) $Y$ is a sequence-covering compact image of a space with a weaker metric topology if and only if $Y$ has a sequence $\{\mathcal F_i\}_{i\in \mathbb N}$ of point-finite $cs$-covers such that $ {\bigcap _{i\in \mathbb N}}\mathop{\rm st} (y,\mathcal F_i)=\{y\}$ for each $y\in Y$. \endgraf (2) $Y$ is a sequentially-quotient compact image of a space with a weaker metric topology if and only if $Y$ has a sequence $\{\mathcal F_i\}_{i\in \mathbb N}$ of point-finite $cs^*$-covers such that ${\bigcap _{i\in \mathbb N}}\mathop{\rm st} (y,\mathcal F_i)=\{y\}$ for each $y\in Y$. (English) |
| Keyword:
|
sequence-covering mappings |
| Keyword:
|
sequentially-quotient mappings |
| Keyword:
|
compact mappings |
| Keyword:
|
weaker metric topology |
| MSC:
|
54C10 |
| MSC:
|
54C40 |
| MSC:
|
54E99 |
| idZBL:
|
Zbl 1174.54022 |
| idMR:
|
MR2471157 |
| . |
| Date available:
|
2010-07-21T08:05:28Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140431 |
| . |
| Reference:
|
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| . |
