| Title:
|
More on $\kappa$-Ohio completeness (English) |
| Author:
|
Basile, D. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
52 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
551-559 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study closed subspaces of $\kappa$-Ohio complete spaces and, for $\kappa$ uncountable cardinal, we prove a characterization for them. We then investigate the behaviour of products of $\kappa$-Ohio complete spaces. We prove that, if the cardinal $\kappa^+$ is endowed with either the order or the discrete topology, the space $(\kappa^+)^{\kappa^+}$ is not $\kappa$-Ohio complete. As a consequence, we show that, if $\kappa$ is less than the first weakly inaccessible cardinal, then neither the space $\omega^{\kappa^+}$, nor the space $\mathbb{R}^{\kappa^+}$ is $\kappa$-Ohio complete. (English) |
| Keyword:
|
$\kappa$-Ohio complete |
| Keyword:
|
compactification |
| Keyword:
|
subspace |
| Keyword:
|
product |
| MSC:
|
54B05 |
| MSC:
|
54B10 |
| MSC:
|
54D35 |
| idZBL:
|
Zbl 1249.54022 |
| idMR:
|
MR2863998 |
| . |
| Date available:
|
2011-12-16T14:05:42Z |
| Last updated:
|
2015-02-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141744 |
| . |
| Reference:
|
[1] Arhangel'skii A.V.: Remainders in compactifications and generalized metrizability properties.Topology Appl. 150 (2005), 79–90. Zbl 1075.54012, MR 2133669, 10.1016/j.topol.2004.10.015 |
| Reference:
|
[2] Basile D.: $\kappa $-Ohio completenss and related problems.Doctoral Thesis, Vrije Universiteit, Amsterdam, 2009. |
| Reference:
|
[3] Basile D., van Mill J.: Ohio completeness and products.Topology Appl. 155 (2008), no. 4, 180–189. Zbl 1147.54012, MR 2380256, 10.1016/j.topol.2007.09.005 |
| Reference:
|
[4] Basile D., van Mill J., Ridderbos G.J.: Sum theorems for Ohio completeness.Colloq. Math. 113 (2008), 91–104. Zbl 1149.54014, MR 2399666, 10.4064/cm113-1-6 |
| Reference:
|
[5] Basile D., van Mill J., Ridderbos G.J.: $\kappa $-Ohio completeness.J. Math. Soc. Japan 61 (2009), no. 4, 1293–1301. Zbl 1186.54024, MR 2588512, 10.2969/jmsj/06141293 |
| Reference:
|
[6] Engelking R.: General Topology.second ed., Heldermann, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[7] Glicksberg I.: Stone-Čech compactifications of products.Trans. Amer. Math. Soc. 90 (1959), 369–382. Zbl 0089.38702, MR 0105667 |
| Reference:
|
[8] Mycielski J.: $\alpha $-incompactness of $N^\alpha $.Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 12 (1964), 437–438. MR 0211871 |
| Reference:
|
[9] Okunev O., Tamariz-Mascarúa A.: On the Čech number of $C_p(X)$.Topology Appl. 137 (2004), no. 1–3, 237–249; IV Iberoamerican Conference on Topology and its Applications. Zbl 1048.54010, MR 2057890, 10.1016/S0166-8641(03)00213-X |
| . |
