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arXiv · 1712.04576

Diffeological, Fr\"{o}licher, and Differential Spaces

Augustin Batubenge·Yael Karshon·Jordan Watts
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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 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.

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Augustin Batubenge, Yael Karshon, Jordan Watts. 2017-12-13. Diffeological, Fr\"{o}licher, and Differential Spaces. https://arxiv.org/abs/1712.04576

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