I am reading a paper on the Myerson Value and it contains the following two definitions which I am having some trouble with:
Let $(N,L)$ be a network (with nodes $N$ and edges $L$).
1) A subset $S \subseteq N$ is said to be connected in $(N,L)$ if $(S,L\vert_S)$ is connected where $L\vert_S = \{l\in L: l\subseteq S\}$
2) A set $S'\subseteq N$ is called a connection set for $S\subseteq N$ if $S\subseteq S'$ and $S$ is connected in $(S',L\vert_{S'})$
Under these definitions isnt it true that the following holds?
a) When $S$ is connected in $(N,L)$ then any $S'\subseteq N$ that is a superset of $S$ will be a connection set for $S$.
b) When $S$ is not connected in $(N,L)$ then it has no connection sets.
This seems wrong by the way it is written and makes me feel I have a fundamental misunderstanding somewhere. Thank you.