| Title:
|
Some results on spaces with $\aleph_1$-calibre (English) |
| Author:
|
Xuan, Wei-Feng |
| Author:
|
Shi, Wei-Xue |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
131-134 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that, assuming \emph{CH}, if $X$ is a space with $\aleph_1$-calibre and a zeroset diagonal, then $X$ is submetrizable. This gives a consistent positive answer to the question of Buzyakova in Observations on spaces with zeroset or regular $G_\delta$-diagonals, Comment. Math. Univ. Carolin. 46 (2005), no. 3, 469--473. We also make some observations on spaces with $\aleph_1$-calibre. (English) |
| Keyword:
|
$\aleph_1$-calibre |
| Keyword:
|
star countable |
| Keyword:
|
zeroset diagonal |
| MSC:
|
54D20 |
| MSC:
|
54E35 |
| idZBL:
|
Zbl 06562203 |
| idMR:
|
MR3478346 |
| DOI:
|
10.14712/1213-7243.2015.154 |
| . |
| Date available:
|
2016-04-12T05:11:00Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144922 |
| . |
| Reference:
|
[1] Buzyakova R.Z.: Observations on spaces with zeroset or regular $G_\delta$-diagonals.Comment. Math. Univ. Carolin. 46 (2005), no. 3, 469–473. MR 2174525 |
| Reference:
|
[2] Buzyakova R.Z.: Cardinalities of ccc-spaces with regular $G_\delta$-diagonals.Topology Appl. 153 (2006), no. 11, 1696–1698. MR 2227022, 10.1016/j.topol.2005.06.004 |
| Reference:
|
[3] Basile D., Bella A., Ridderbos G.J.: Weak extent, submetrizability and diagonal degrees.Houston J. Math. 40 (2014), no. 1, 255–266. MR 3210565 |
| Reference:
|
[4] Engelking R.: General Topology.Heldermann, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[5] Ikenaga S.: A class which contains Lindelöf spaces, separable spaces and countably compact spaces.Memoirs of Numazu College of Technology 18 (1983), 105–108. |
| Reference:
|
[6] Martin H.W.: Contractibility of topological spaces onto metric spaces.Pacific J. Math. 61 (1975), no. 1, 209–217. MR 0410685, 10.2140/pjm.1975.61.209 |
| Reference:
|
[7] Wage M.L., Fleissner W.G., Reed G.M.: Normality versus countable paracompactness in perfect spaces.Bull. Amer. Math. Soc. 82 (1976), no. 4, 635–639. MR 0410665, 10.1090/S0002-9904-1976-14150-X |
| Reference:
|
[8] Tall F.D.: First Countable Space with $\aleph_1$-Calibre May or May not be Separable.Set-theoretic Topology, Academic Press, New York, 1977. MR 0500795 |
| . |
