Cycle spaces in topological spaces

We develop a general model of edge spaces in order to generalize, unify, and simplify previous work on cycle spaces of infinite graphs. We give simple topological criteria to show that the fundamental cycles of a (generalization of a) spanning tree generate the cycle space in a connected, compact, weakly Hausdorff edge space. Furthermore, in such a space, the orthogonal complement of the bond space is the cycle space. This work unifies the two different notions of cycle space as introduced by Diestel and Kühn (Combinatorica 24 (2004), 68–89 and Europ. J. Combin. 25 (2004), 835–862) and by Bonnington and Richter (J. Graph Theory 44 (2003), 132–147).