| Title:
|
The product of two ordinals is hereditarily dually discrete (English) |
| Author:
|
Gaspar-Arreola, M.Á. |
| Author:
|
Hernández-Hernández, F. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
99-104 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In Dually discrete spaces, Topology Appl. 155 (2008), 1420--1425, Alas et. al. proved that ordinals are hereditarily dually discrete and asked whether the product of two ordinals has the same property. In Products of certain dually discrete spaces, Topology Appl. 156 (2009), 2832--2837, Peng proved a number of partial results and left open the question of whether the product of two stationary subsets of $\omega_1$ is dually discrete. We answer the first question affirmatively and as a consequence also give a positive answer to the second. (English) |
| Keyword:
|
dually discrete spaces |
| Keyword:
|
stationary subsets |
| Keyword:
|
ordinal spaces |
| MSC:
|
54D99 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 1249.54051 |
| idMR:
|
MR2880913 |
| . |
| Date available:
|
2012-02-07T10:26:19Z |
| Last updated:
|
2014-04-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141828 |
| . |
| Reference:
|
[1] Alas O.T., Junqueira L.R., Wilson R.G.: Dually discrete spaces.Topology Appl. 155 (2008), 1420–1425. Zbl 1169.54010, MR 2427413, 10.1016/j.topol.2008.04.003 |
| Reference:
|
[2] Buzyakova R.Z., Tkachuk V.V., Wilson R.G.: A quest for nice kernels of neighbourhood assignments.Comment. Math. Univ. Carolin. 48 (2007), no. 4, 689–697. Zbl 1199.54141, MR 2375169 |
| Reference:
|
[3] van Douwen E.K., Pfeffer W.F.: Some properties of the Sorgenfrey line and related spaces.Pacific J. Math. 81 (1979), no. 2, 371–377. Zbl 0409.54011, MR 0547605, 10.2140/pjm.1979.81.371 |
| Reference:
|
[4] van Mill J., Tkachuk V.V., Wilson R.G.: Classes defined by stars and neighborhood assignments.Topology Appl. 154 (2007), 2127–2134. MR 2324924, 10.1016/j.topol.2006.03.029 |
| Reference:
|
[5] Peng L.X.: Dual properties of subspaces in product of ordinals.Topology Appl. 157 (2010), 2297–2303. MR 2670506, 10.1016/j.topol.2010.06.010 |
| Reference:
|
[6] Peng L.X.: Finite unions of weak $\bar{\theta}$-refinable spaces and product of ordinals.Topology Appl. 156 (2009), 1679–1683. MR 2521704, 10.1016/j.topol.2009.01.013 |
| Reference:
|
[7] Peng L.X.: Products of certain dually discrete spaces.Topology Appl. 156 (2009), 2832–2837. Zbl 1180.54029, MR 2556039, 10.1016/j.topol.2009.08.018 |
| . |
