The multiplication sign 
is used to denote multiplication,
i.e., 
denotes 
times 
.
The symbol 
is also used to denote a group direct product,
a Cartesian product, or a direct
product in the appropriate category (such as a Cartesian product of manifolds
when it is implied that the smooth structure
is the natural product structure). The similar symbol 
is reserved for a tensor
product, which occurs for representations,
bundles, and modules.
