| Title:
|
Observations on spaces with zeroset or regular $G_\delta$-diagonals (English) |
| Author:
|
Buzyakova, Raushan Z. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
469-473 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that if $X^2$ has countable extent and $X$ has a zeroset diagonal then $X$ is submetrizable. We also make a couple of observations regarding spaces with a regular $G_\delta$-diagonal. (English) |
| Keyword:
|
zeroset diagonal |
| Keyword:
|
regular $G_\delta$-diagonal |
| Keyword:
|
submetrizable |
| Keyword:
|
countable extent |
| MSC:
|
54A25 |
| MSC:
|
54E35 |
| MSC:
|
54E99 |
| idZBL:
|
Zbl 1121.54051 |
| idMR:
|
MR2174525 |
| . |
| Date available:
|
2009-05-05T16:52:34Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119541 |
| . |
| Reference:
|
[ARH] Arhangelskii A.V.: On a class of spaces containing all metric spaces and all locally compact spaces.Mat. Sb 67 (1965), English Translation: Amer. Math. Soc. Transl. 92 (1970), 1-39. MR 0190889 |
| Reference:
|
[ENG] Engelking R.: General Topology.Sigma Series in Pure Mathematics, 6, Heldermann, Berlin, revised ed., 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[FRW] Fleissner W.G., Reed G.M., Wage M.L.: Normality versus countable paracompactness in perfect spaces.Bull. Amer. Math. Soc. 82 4 (1976), 635-639. Zbl 0332.54018, MR 0410665 |
| Reference:
|
[KAR] Karpov A.N.: Countable products of Čech-complete linearly Lindelöf and initially-compact spaces.Vestnik Moskov. Univ. Ser. I Mat. Mekh. (2000), 5 7-9, 67. Zbl 0984.54006, MR 1799346 |
| Reference:
|
[MAR] Martin H.W.: Contractibility of topological spaces onto metric spaces.Pacific J. Math. 61 (1975), 1 209-217. Zbl 0304.54026, MR 0410685 |
| . |
