Relating different cycle spaces of the same infinite graph (Q547795)

Summary: Casteels and Richter have shown that if \(X\) and \(Y\) are distinct compactifications of a locally finite graph \(G\) and \(f : X \rightarrow Y\) is a continuous surjection such that \(f\) restricts to a homeomorphism on \(G\), then the cycle space \(Z_X\) of \(X\) is contained in the cycle space \(Z_Y\) of \(Y\). In this work, we show how to extend a basis for \(Z_X\) to a basis of \(Z_Y\) .