Productivity of paracompactness in the class of GO-spaces

The main result of the paper says that if X is a paracompact GO-space, meaning a subspace of a linearly ordered space and M a paracompact space satisfying the first axiom of countability such that X can be embedded in Mω1 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 has a winning strategy. In particular we obtain that if X is paracompact GO-space of weight not greater than ω1 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 has a winning strategy.