Earlier today I was going through an old text at my university's library which uses the Big X symbol with sub- and super-scripts (I believe in LaTeX this would be \varprod or \bigtimes, but it seems the package is not supported here), and I am curious on what this is notation for. I wish I wrote down the title of the book but sadly I cannot remember it. However, I do recall he context, which was that we have individual spaces $X_i$, then the author defines a new space as $ X = \mathop{\large\times}\limits_{i=1}^n X_i $.
At first I thought this was the same as taking a Cartesian product, but he used the usual $\prod$ symbol for that further down the page, so I am inclined to believe there is some difference. Does anyone know what it is?
This old SE question shows the symbol I am referring to, but sadly does not provide an explanation.
It is either Cartesian product for sets or direct product (for algebraic structures). The big pi is more generally used and its dual notion of coproduct uses the upsidedown symbol, $\coprod$. When one does not care about the baggage of the universal properties, the original notation is fine. Other uses of pi are for construction of terms (say as in the determinant formula).