Mayer-Vietoris sequence for generating families in diffeological spaces

TL;DR

This paper extends the Mayer-Vietoris sequence to diffeological spaces using generating families, broadening the applicability of differential form techniques beyond traditional topological coverings.

Contribution

It introduces a novel approach replacing open coverings with generating families to establish Mayer-Vietoris sequences in diffeological spaces.

Findings

Mayer-Vietoris sequence is valid for diffeological spaces with generating families.

The approach generalizes classical results to a broader class of spaces.

Provides a new tool for computing de Rham cohomology in diffeological spaces.

Abstract

We prove a version of the Mayer-Vietoris sequence for De Rham differential forms in diffeological spaces. It is based on the notion of a generating family instead of that of a covering by open subsets.