We consider sets of reals X endowed with the Sorgenfrey lower limit topology denoted $X[\leq]$. Przymusinski proved that if X is a Q-set then $(X[\leq])^2$ is normal. Todorčević proved if X is an entangled set, then all finite power of $X[\leq]$ are hereditarily Lindelöf, hence $(X[\leq])^2$ is normal.

We construct from CH a subset X of reals, such that X is not a $\lambda$-set (hence not a Q-set), X is not 2-entangled, but still $(X[\leq])^2$ is normal.

We will also prove the easy analogue of Przymusinski’s theorem for $\lambda$-sets. i.e. if X is a $\lambda$-set then $(X[\leq])^2$ is pseudo-normal.