Countable products of absolute C-delta spaces

It is shown that countable products of completely regular absolute C-delta spaces inherit each of the following properties from their factors: paracompactness, Lindelofness, metacompactness and ultra-paracompactness. This generalizes previous results by Z. Frolik, by K. Alster, by M.E. Rudin and S. Watson, by L.M. Friedler, H.W. Martin and S.W. Williams, and by A. Hohti and Y. Ziqui. The proof uses ideas from localic topology. Completely regular absolute C-delta's (spaces which are C-delta subspaces of every extension) are characterized as the partition complete spaces of R. Telgarsky and H.H. Wicke. A subspace is called C-delta if it is a countable intersection of complemented subspaces, and a subspace C is complemented if for every nonempty closed subspace F not both C boolean AND F and F \ C are dense in F. The class of completely regular absolute C-delta's shares many properties with the class of absolute G(delta)'s (closed under countable products, direct and inverse images along perfect maps) and even improves on some, for instance, it is closed under open images.