# On subcartesian spaces Leibniz' rule implies the chain rule

## TL;DR

This paper proves that derivations on subcartesian spaces obey the chain rule and possess maximal integral curves, extending the understanding of differential structures in these spaces.

## Contribution

It establishes that derivations in subcartesian spaces satisfy the chain rule and have maximal integral curves, providing new insights into their differential structure.

## Key findings

- Derivations satisfy the chain rule.
- Existence of maximal integral curves.
- Extension of differential calculus to subcartesian spaces.

## Abstract

We show that derivations of the differential structure of a subcartesian space satisfy the chain rule and have maximal integral curves.