Couplings and primitives on topological spaces
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2022
- DOI:
- 10.48550/arXiv.2204.08969
- arXiv:
- arXiv:2204.08969
- Bibcode:
- 2022arXiv220408969V
- Keywords:
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- Mathematics - Functional Analysis;
- 54C20;
- 46F10;
- 55U99