What does the multiply sign mean in set

Question

A question about set notation. What does the multiply sign here mean?

$$\omega = \times_{i\in N}T_{i}$$

Answer 1

That is occasionally used as an alternative for $\prod$, meaning an indexed Cartesian product.

From the Wikipedia article on Cartesian products:

Answer 2

Whenever you see a usual symbol you know with a subscript telling you that a variable belongs to a set, it means to carry out that operation on everything with that variable as it's index. You have seen this before likely in the form of summation with big sigma notation. In this case, it means to take the Cartesian product (i.e. form ordered tuples by taking one element from each set) over each of the $T_i$'s.