We prove a Kunneth theorem for the Vietoris-Rips homology and cohomology of a semi-uniform space. We then interpret this result for graphs, where we show that the Kunneth theorem holds for graphs with respect to the strong graph product. We finish by computing the Vietoris-Rips cohomology of the torus endowed with diferent semi-uniform structures.

中文翻译：

---

Vietoris-Rips同调的Kunneth定理

我们证明了半均匀空间的 Vietoris-Rips 同调和上同调的 Kunneth 定理。然后我们将这个结果解释为图，我们证明了关于强图乘积的图，Kunneth 定理成立。我们通过计算具有不同半均匀结构的环面的 Vietoris-Rips 上同调来完成。