The product of two ordinals is hereditarily dually discrete
M.Á. Gaspar-Arreola; F. Hernández-Hernández
Commentationes Mathematicae Universitatis Carolinae (2012)
- Volume: 53, Issue: 1, page 99-104
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topGaspar-Arreola, M.Á., and Hernández-Hernández, F.. "The product of two ordinals is hereditarily dually discrete." Commentationes Mathematicae Universitatis Carolinae 53.1 (2012): 99-104. <http://eudml.org/doc/246121>.
@article{Gaspar2012,
abstract = {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.},
author = {Gaspar-Arreola, M.Á., Hernández-Hernández, F.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {dually discrete spaces; stationary subsets; ordinal spaces; dually discrete space; stationary set; ordinal space},
language = {eng},
number = {1},
pages = {99-104},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The product of two ordinals is hereditarily dually discrete},
url = {http://eudml.org/doc/246121},
volume = {53},
year = {2012},
}
TY - JOUR
AU - Gaspar-Arreola, M.Á.
AU - Hernández-Hernández, F.
TI - The product of two ordinals is hereditarily dually discrete
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 1
SP - 99
EP - 104
AB - 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.
LA - eng
KW - dually discrete spaces; stationary subsets; ordinal spaces; dually discrete space; stationary set; ordinal space
UR - http://eudml.org/doc/246121
ER -
References
top- Alas O.T., Junqueira L.R., Wilson R.G., 10.1016/j.topol.2008.04.003, Topology Appl. 155 (2008), 1420–1425. Zbl1169.54010MR2427413DOI10.1016/j.topol.2008.04.003
- 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. Zbl1199.54141MR2375169
- van Douwen E.K., Pfeffer W.F., 10.2140/pjm.1979.81.371, Pacific J. Math. 81 (1979), no. 2, 371–377. Zbl0409.54011MR0547605DOI10.2140/pjm.1979.81.371
- van Mill J., Tkachuk V.V., Wilson R.G., 10.1016/j.topol.2006.03.029, Topology Appl. 154 (2007), 2127–2134. MR2324924DOI10.1016/j.topol.2006.03.029
- Peng L.X., 10.1016/j.topol.2010.06.010, Topology Appl. 157 (2010), 2297–2303. MR2670506DOI10.1016/j.topol.2010.06.010
- Peng L.X., 10.1016/j.topol.2009.01.013, Topology Appl. 156 (2009), 1679–1683. MR2521704DOI10.1016/j.topol.2009.01.013
- Peng L.X., 10.1016/j.topol.2009.08.018, Topology Appl. 156 (2009), 2832–2837. Zbl1180.54029MR2556039DOI10.1016/j.topol.2009.08.018
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.