## Abstract

An I-category consists all Banach manifolds as objects and subclasses of continuous functions (with some kind of smoothness) as morphisms. This notion covers, for example, the categories C^{∞}, C_{n}, C, and Lip_{loc} of all smooth functions, C_{n} -functions, continuous functions, and local Lipschitz functions. It is shown by Garrido, Jaramillo and Prieto in 2000 that two C^{∞} -smooth Banach manifolds X and Y are C^{∞} -diffeomorphic to each other if and only if there is an algebra isomorphism from C^{∞}(X,R) onto C^{∞}(Y,R). We extend this result to general abstract I-categories, and from algebra isomorphisms of scalar functions to the maps which are linear, bijective and separating, between vector-valued functions.

Original language | English |
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Pages (from-to) | 715-724 |

Number of pages | 10 |

Journal | Operators and Matrices |

Volume | 6 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 2012 |

## Scopus Subject Areas

- Analysis
- Algebra and Number Theory

## User-Defined Keywords

- I-category
- Lipschitz function
- Separating map
- Smooth functions