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

Characterization of ω 1 -metrizable spaces whose product with every paracompact space is paracompact, is given. We proved that this class coincides with the class of all ω 1 -metrizable spaces whose product with every paracompact space is normal. It is shown that if X belongs to the above mentioned class then X ω is paracompact. Also if Z is an ω 1 -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.