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 H1. This homology seems to be particularly apt for studying spaces with infinitely generated H1, e.g. infinite graphs or fractals.

中文翻译：

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循环分解：从图形到连续体

我们将一个基本的图论事实概括为任意连续体，即图的循环空间的每个元素都是边不相交循环的总和。为了实现这一点，我们用拓扑圆替换图循环，并用一个新的连续同调群替换图的循环空间，连续体是第一个奇异同调群 H1 的商。这种同源性似乎特别适合研究具有无限生成 H1 的空间，例如无限图或分形。