In topology, there is a very strong need of describing subsets of some product $X\times Y$ by means of unions and products.
For example, this is a very convenient way of describing subsets of the plane. (Which are common examples in, say, algebraic topology.)
Is there any standard convention about the precedence of products and unions?
In particular, when I write $A\times B\cup C\times D$ would this be interpreted as $A\times(B\cup C)\times D$ or as $(A\times B)\cup(C\times D)$? I personally would go with the second option, because of the analogy with multiplication and addition, which for some reason seems to make sense to me. (And in that case there is a standard convention). Despite this analogy, I fear the omission of parentheses in the case of sets might be ambiguous to some people.
Is it better to always use parentheses?
(Of course a downside of parentheses would be that the notation may become very cluttered, when the expressions are long.)