Compactly Choquet-complete spaces III: products and continuous almost open images

We continue our study of the class of compactly Choquet-complete spaces. We will show two things. First, that this class is closed under finite and countable products, but not under arbitrary products. While the technique for finite products consists in simulating plays in every space in parallel, the technique for countable products is a bit more subtle, and requires us to start the simulation of each individual game with a variable delay. Second, we will see that images of compactly Choquet-complete spaces under continuous, almost open maps, are still compactly Choquet-complete spaces, similarly to the cases of Choquet-complete and convergence Choquet-complete spaces, as dealt with in the book. Read the full post.