圈分解：从图到连续统
Cycle decompositions: from graphs to continua
摘要：
我们概括了一个基本的图论事实，指出每个元素的循环空间的一个图是一个总和的边缘不相交的周期，以任意连续。为了实现这一点，我们取代图圈的拓扑圈，并取代一个新的连续统，这是一个商的第一奇异同调群$H_1$的一个图的循环空间。这种同调似乎特别适合于研究具有无限生成的$H_1$的空间，例如无限图或分形。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
