Notation for sets that do not overlap Is there notation to describe, say a set that consists entirely of two mutually exclusive subsets?
Say $ D = D_1 \cup D_2 $, how to indicate that $D_1$ and $D_2$ do not overlap?

$D_1 \sqcup D_2$ and $D_1 \stackrel{\circ}\cup D_2$ [possibly with the circle or dot lower within the 'cup'] are both used, to denote the union of $D_i$ when you want to emphasize that the $D_i$ are disjoint. Sometimes "disjoint union" is meant to be an operation in its own right, guaranteeing disjointness of the operands before forming their union. For example, 
$$
D_1 \sqcup D_2 := \{0\}\times D_1 \cup \{1\}\times D_2.
$$ 
In either case, an author will (should) make clear what the symbol will denote.
