On nonnormal products and a set of A.H. Stone

A variant of Michaelʹs example is given to the following effect: there is a Lindelöf space M of weight ℵ 1 , with all G δ -sets open, such that M × B ( ℵ 1 ) is nonnormal. This answers a question from [K. Alster, On the class of ω 1 -metrizable spaces whose product with every paracompact space is paracompact, Topology Appl. 153 (2006) 2508–2517].