Is a vertex comparable to itself in a DAG (directed acyclic graph)? The definition offered in Mathematics for Computer Science is not very clear. (This definition is Definition 10.5.5. in page 381 [or page 389 in the pdf file]). Additionally, is the empty set of vertices of a DAG a chain? It would be great if someone can offer a better definition for comparability of vertices and chains in a DAG.
My suspicion is that a vertex is comparable to itself, and the empty set is a chain.
The authors of that lengthy work define comparable in terms of reachable, which is itself defined in terms of a walk or directed path. Their wording seems to me to allow a vertex to be reachable from itself (by a walk of zero length).