Lindelöf spaces concentrated on Bernstein subsets of the real line

Abstract

We show in ZFC that for each n n with n ∈ ω n \in \omega or n = ω n = \omega , there is a Lindelöf space X X and a separable metric space M M such that for every m > n m > n , X × m M X \times {}^mM is Lindelöf, whereas X × n M X \times {}^nM is nonnormal.