  We generalise a fundamental graph-theoretical fact, stating that every
element of the cycle space of a graph is a sum of edge-disjoint cycles, to
arbitrary continua. To achieve this we replace graph cycles by topological
circles, and replace the cycle space of a graph by a new homology group for
continua which is a quotient of the first singular homology group $H_1$. This
homology seems to be particularly apt for studying spaces with infinitely
generated $H_1$, e.g. infinite graphs or fractals.
