# Article

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Keywords:
dually discrete spaces; stationary subsets; ordinal spaces
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.
References:
[1] Alas O.T., Junqueira L.R., Wilson R.G.: Dually discrete spaces. Topology Appl. 155 (2008), 1420–1425. DOI 10.1016/j.topol.2008.04.003 | MR 2427413 | Zbl 1169.54010
[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. MR 2375169 | Zbl 1199.54141
[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. DOI 10.2140/pjm.1979.81.371 | MR 0547605 | Zbl 0409.54011
[4] van Mill J., Tkachuk V.V., Wilson R.G.: Classes defined by stars and neighborhood assignments. Topology Appl. 154 (2007), 2127–2134. DOI 10.1016/j.topol.2006.03.029 | MR 2324924
[5] Peng L.X.: Dual properties of subspaces in product of ordinals. Topology Appl. 157 (2010), 2297–2303. DOI 10.1016/j.topol.2010.06.010 | MR 2670506
[6] Peng L.X.: Finite unions of weak $\bar{\theta}$-refinable spaces and product of ordinals. Topology Appl. 156 (2009), 1679–1683. DOI 10.1016/j.topol.2009.01.013 | MR 2521704
[7] Peng L.X.: Products of certain dually discrete spaces. Topology Appl. 156 (2009), 2832–2837. DOI 10.1016/j.topol.2009.08.018 | MR 2556039 | Zbl 1180.54029

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