On the class of ω1-metrizable spaces whose product with every paracompact space is paracompact

AbstractCharacterization of ω1-metrizable spaces whose product with every paracompact space is paracompact, is given. We proved that this class coincides with the class of all ω1-metrizable spaces whose product with every paracompact space is normal. It is shown that if X belongs to the above mentioned class then Xω is paracompact. Also if Z is an ω1-metrizable closed image of X then Z belongs to the above mentioned class. Some other results related to the questions of R. Telgarsky are presented