Products of Lindelöf spaces and GO-spaces

Abstract

We prove that if X is a paracompact monotonically normal space, and Y has a point-countable base, then X × Y is meta-Lindelöf. It follows from results of Alster and Lawrence that, assuming b > ω1, if X is a Lindelöf monotonically normal space and ωω is the space of irrationals, then X × ωω is Lindelöf. We also consider the following problem: Are there in ZFC Lindelöf spaces X and Y such that every uncountable subset of X × Y has a condensation point, but X × Y is not Lindelöf? We show that there are examples of such X and Y assuming c > ω1, and it is consistent that there are examples with X and Y hereditarily Lindelöf. We prove (in ZFC) that there are no examples where X is a Lindelöf GO-space and Y is hereditarily Lindelöf. © 1995.