Normality in k-and-ℵ spaces

AbstractWe give examples to show that a k-and-ℵ space need not be normal and that, under MA+¬CH, a k-and-ℵ0 space need not be monotonically normal. We give several sufficient conditions for the monotone normality of a k-and-ℵ space which involve local properties, coverings by compact sets, and sequential order. Finally, we show that a normal k-and-ℵ space is paracompact