I'm interested in the game-characterization proposed by Telgarsky (paper) of the class of paracompact spaces that preserve paracompactness under cartesian product with another paracompact space. He uses a game $G(\mathbb{DC},X)$ defined over the class of disjoint unions of compact sets. In particular I'm interested only in the proved implication, that is:
If X is paracompact and $\mathbb{DC}$-like, then X × Y is paracompact for all paracompact spaces Y .
Telgársky, Rastislav, Spaces defined by topological games, Fundam. Math. 88, 193-223 (1975). ZBL0311.54025.)
Do you know if the proof of this theorem appears in a somewhat more intelligible and elegant way in a more recent paper\presentation\notes etc.? Thanks