A remark on stability and the D-topology of mapping spaces

Abstract

We discuss how stability is related to the D-topology of mapping spaces, equipped with the functional diffeology. Indeed, we show that stable classes of mapping spaces are D-open. After a reformulation of the classical stability theorem of manifolds with respect to the D-topology, we prove a version of the stability theorem in the class of diffeological étale manifolds.

arXiv admin note: text overlap with arXiv:2203.05994