I suggest renaming this to "countably factored spaces". Countably being a property of the factorization rather than the space.
Also I suggest adding an actual self-contained definition of countable factored space to make it more readable.
Note that the title is misleading. This is really countable dimension factored spaces, which is much better, since it allows for the possibility of something kind of like continuous time, where between any two points in time, you can specify a time strictly between them.