Does 'a graph is a DAG $\iff$ there exists a topological sorting' hold for graphs with a non-finite number of nodes?
I see this statement at a lot of places e.g. wiki. However it is not specified whether the graphs are finite.
The accompanying definitions are: DAG = directed and acyclic. A topological sorting is a linear ordering of the nodes such that for each edge $uv$, the node $u$ comes before $v$ in the ordering.
Could the answer be a related to the axiom of choice?
According to wiki: partial orders. Every strict partial order is a DAG. And the transitive closure of a DAG is a DAG and a strict partial order. (Which might help in the connection with choice)