PERFECT KAPPA-NORMALITY OF PRODUCT-SPACES

A space X is called perfectly kappa-normal (respectively, Klebanov) if the closure of every open set (respectively, every union of zero-sets) in X is a zero-set. It is proved: The product of infinitely many Lasnev spaces need not be perfectly kappa-normal, in particular, S(omega(1))(2) x D-omega 1 is not perfectly kappa-normal; a locally compact, paracompact space Y is Klebanov if and only if X x Y is perfectly kappa-normal for every Lasnev space X; if X x Y is perfectly kappa-normal for every paracompact sigma-space X, then Y is perfectly normal. Properties of a Klebanov space are also studied.