Another note on the class of paracompact spaces whose product with every paracompact space is paracompact

摘要

The paper contains the following two results: (1) If X is a paracompact space and M is a metric space such that X can be embedded in M~(ω1) in such a way that the projections of X onto initial countably many coordinates are closed, then the product X × Y is paracompact for every paracompact space Y if and only if the first player of the G(DC, X) game, introduced by Telgarsky, see Telgarsky (1975) [22). has a winning strategy. (2) If X is paracompact space, Y is a closed image of X and the first player of the G(DC, X) game has a winning strategy then also the first player of the G(DC, Y) game has a winning strategy.