Diffeological, Frölicher, and Differential Spaces

Abstract

Differential calculus on Euclidean spaces has many generalisations. In particular, on a set $X$, a diffeological structure is given by maps from open subsets of Euclidean spaces to $X$, a differential structure is given by maps from $X$ to $\mathbb{R}$, and a Frölicher structure is given by maps from $\mathbb{R}$ to $X$ as well as maps from $X$ to $\mathbb{R}$. We illustrate the relations between these structures through examples.

37 pages; v2 has more examples, results on underlying topologies, and an appendix summarizing relationships with other smooth structures

Cited by in corpus (1)

• Smooth Banach structure on orbit spaces and leaf spaces