Diffeological Spaces with a Non-Smooth Derivation
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910032536272896 |
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| author | Taho, Masaki |
| author_facet | Taho, Masaki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21235 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Diffeological Spaces with a Non-Smooth Derivation Taho, Masaki Differential Geometry Algebraic Topology 57P05 (Primary) 58A05 (Secondary) 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. |
| title | Diffeological Spaces with a Non-Smooth Derivation |
| topic | Differential Geometry Algebraic Topology 57P05 (Primary) 58A05 (Secondary) |
| url | https://arxiv.org/abs/2602.21235 |