We show linear derivations on diffeological spaces that satisfy the Leibniz rule, highlighting implications for tangent space definitions.
We show that on certain diffeological spaces there exist linear derivations that satisfy the Leibniz rule but are not smooth with respect to the given diffeology. This reveals that the notion of tangent space defined via all such derivations is strictly larger than the one defined using only smooth derivations, showing that smoothness cannot be recovered from the Leibniz rule alone.
No takes yet. Share an insight, caveat, or question.
Masaki Taho (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: