| Title:
|
Closed mapping theorems on $k$-spaces with point-countable $k$-networks (English) |
| Author:
|
Shibakov, A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
77-87 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove some closed mapping theorems on $k$-spaces with point-countable $k$-networks. One of them generalizes La\v snev's theorem. We also construct an example of a Hausdorff space $Ur$ with a countable base that admits a closed map onto metric space which is not compact-covering. Another our result says that a $k$-space $X$ with a point-countable $k$-network admitting a closed surjection which is not compact-covering contains a closed copy of $Ur$. (English) |
| Keyword:
|
$k$-space |
| Keyword:
|
$k$-network |
| Keyword:
|
closed map |
| Keyword:
|
compact-covering map |
| MSC:
|
54A20 |
| MSC:
|
54B10 |
| MSC:
|
54C10 |
| idZBL:
|
Zbl 0832.54011 |
| idMR:
|
MR1334416 |
| . |
| Date available:
|
2009-01-08T18:16:10Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118734 |
| . |
| Reference:
|
[A] Arkhagel'skii A.: Factor mappings of metric spaces (in Russian).Dokl. Akad. Nauk SSSR 155 (1964), 247-250. MR 0163284 |
| Reference:
|
[GMT] Gruenhage G., Michael E., Tanaka Y.: Spaces determined by point-countable covers.Pacif. J. Math. 113 (1984), 303-332. Zbl 0561.54016, MR 0749538 |
| Reference:
|
[H] Hoshina T.: On the quotient $s$-images of metric spaces.Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 10 (1970), 265-268. Zbl 0214.49503, MR 0275358 |
| Reference:
|
[L] Lašnev N.: Continuous decompositions and closed mappings of metric spaces.Sov. Math. Dokl. 6 (1965), 1504-1506. MR 0192478 |
| Reference:
|
[M] Michael E.: $\aleph_0$-spaces.J. Math. Mech. 15 (1966), 983-1002. MR 0206907 |
| Reference:
|
[Miš] Miščenko A.: Spaces with pointwise denumerable basis (in Russian).Dokl. Akad. Nauk SSSR 145 (1962), 985-988 Soviet Math. Dokl. 3 (1962), 855-858. MR 0138090 |
| Reference:
|
[T] Tanaka Y.: Point-countable covers and $k$-networks.Topology Proceedings 12 (1987), 327-349. Zbl 0676.54035, MR 0991759 |
| Reference:
|
[V1] Velichko N.: Ultrasequential spaces (in Russian).Mat. Zametki 45 (1989), 15-21. MR 1002513 |
| Reference:
|
[V2] Velichko N.: On continuous mappings of topological spaces (in Russian).Sibirsky Mat. Zhurnal 8 (1972), 541-557. MR 0301691 |
| . |
