Difficult# Comparing The Product And Box Topologies

TOPO-JGSYZN

Let $I$ be an index set and $\{X_i\}_{i\in I}$ an indexed family of topological spaces.

If $Y$ denotes $\Pi_{i\in I} X_i$ given the product topology and $Z$ denotes $\Pi_{i\in I} X_i$ given the box topology, which of the following are necessarily **TRUE**?