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Diffeological, Fr\"{o}licher, and Differential Spaces. (arXiv:1712.04576v1 [math.DG])
来源于:arXiv
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 Fr\"{o}licher 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. 查看全文>>