论文标题
拓扑空间上的耦合和原语
Couplings and primitives on topological spaces
论文作者
论文摘要
对于拓扑空间的$ \数学覆盖$ \ MATHCAL U $，以及映射$ d \ colon \ Mathcal I \ to \ Mathbb {k} $，其中$ \ MATHCAL I：= \ bigl \ {（u，v）为所有$（u，v）\ in \ mathcal i $ $ c_v-c_u = $ c_v-c_u = $ c_v-c_u = d_v-c_u = d_v-c_u = d_v-c_u = d $（u，v）\ in \ nathcal i $ $。结果应用于有关分布势的庞加莱型定理。我们还将结果置于代数拓扑的背景下。
For an open covering $\mathcal U$ of a topological space and a mapping $d\colon\mathcal I\to\mathbb{K}$, where $\mathcal I:=\bigl\{(U,V)\in\mathcal U\times\mathcal U;\ U\cap V\ne\varnothing\bigr\}$, we present a context for the existence of a mapping $C\colon\mathcal U\to\mathbb{K}$ satisfying $C_V-C_U=d_{UV}$ for all $(U,V)\in\mathcal I$. The result is applied to a Poincaré type theorem concerning distributional potentials. We also put the result into the context of algebraic topology.
