All Questions

Is it possible to cover $Z^\infty$ (the infinite direct sum of $Z$'s with the $l_1$-metric) by a finite set of collections of subsets $U^0,...,U^n$ such that each collection $U^i$ consists of ...

Let $G$ be an amenable group (so locally compact Hausdorff) and also assume it is second countable if needed. My question is that what are the standard ways (across literature) of defining the upper ...