M.Á. Gaspar-Arreola, F. Hernández-Hernández
The product of two ordinals is hereditarily dually discrete

Comment.Math.Univ.Carolin. 53,1 (2012) 99-104.

Abstract:In {\it Dually discrete spaces\/}, Topology Appl. {\bf 155} (2008), 1420--1425, Alas {\it et.~al.} proved that ordinals are hereditarily dually discrete and asked whether the product of two ordinals has the same property. In {\it Products of certain dually discrete spaces\/}, Topology Appl. {\bf 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.

Keywords: dually discrete spaces, stationary subsets, ordinal spaces
AMS Subject Classification: 54D99 54F05