Given an open covering of a paracompact topological space $X$, there are two natural ways to construct a map from the cohomology of the nerve of the covering to the cohomology of $X$. One of them is based on a partition of unity, and is more topological in nature, while the other one relies on the double complex associated to an open covering, and has a more algebraic flavour. In this paper we prove that these two maps coincide.

中文翻译：

---

关于奇异同调的覆盖物的双重复合体的评论

给定超紧凑拓扑空间$ X $的开放覆盖范围，有两种自然的方法可以构建从覆盖层神经的同调性到$ X $的同调性的地图。其中一个基于统一分区，并且本质上更具拓扑性，而另一个则依赖于与开放覆盖相关的双重复合体，并且具有更多的代数风格。在本文中，我们证明了这两个地图是重合的。