Is there a standard (or commonly used) symbol for the function that switches dimensions of a set?
Formally, I am looking for a symbol for the function $f:\mathcal{P}(A \times B) \to \mathcal{P}(B \times A)$ defined by $$ f(S)=\{(b,a) \mid (a,b) \in S \} $$
Alternatively, a symbol for the function $g:A \times B \to B \times A$ would also be helpful, where $g$ is defined by $$ g(a,b)=(b,a) $$
If there is no standard notation for $f$, reasonable suggestions on what could be a good symbol (or name) for $f$ are also helpful!