I'm a bit confused about the definition of a Petri-Net. From Wikipedia (EN) I have this defintion:
A Petri-Net is a 5-Tupel (P, T, F, W, s)
P and T are disjoint finite sets of places and transitions, respectively.
So the defintion says: $P \cap T = \emptyset $ & $P \cup T \neq \emptyset $
Let's say T is $ \emptyset $ and P = { p } so both prerequisites are given. I think that is okay. We have a system which stays allways in one state and can not change to another so we do not need any other state or transition.
Now think about the other case: T = { t } and P is $ \emptyset $. Now we have a system which does not have a state. The transition can't do anything because we do not have any states and it does not have any meaningful meaning in this case.
So does any Petri-Net which has minimum one transition need two places? Or have I missed out something?