Permissively structured transfinite electrical networks (Q1969538)

The author provides a more natural development of the theory of transfinite electrical networks. Suppose a \(v\)-section is a maximal subnetwork whose nodes are connected by two-ended paths of rank no larger than \(v\). The author defines a suitable metric \(d\) on the node set \(N\) of each \(v\)-section. Taking the completion of \(N\) under \(d\), those extremities that are accessible to current flows are identified. A recursive construction is used through all natural ranks and through the first arrow rank and the first limit-ordinal rank.