### Abstract

We set up differential calculi in the Cartesian-closed category CONV of convergence spaces. The central idea is to uniformly define the 3-place relation_is a differential of_at_for each pair of convergence spaces X, Y in the category, where the first and second arguments are elements of Hom(X, Y) and the third argument is an element of X, in such a way as to (1) obtain the chain rule, (2) have the relation be in agreement with standard definitions from real and complex analysis, and (3) depend only on the convergence structures native to the spaces X and Y. All topological spaces and all reflexive directed graphs (i.e. discrete structures) are included in CONV. Accordingly, ramified hybridizations of discrete and continuous spaces occur in CONV. Moreover, the convergence structure within each space local to each point, individually, can be discrete, continuous, or hybrid.

Original language | English (US) |
---|---|

Title of host publication | Logical Foundations of Computer Science - International Symposium, LFCS 2007, Proceedings |

Pages | 41-53 |

Number of pages | 13 |

State | Published - Oct 29 2007 |

Event | International Symposium on Logical Foundations of Computer Science, LFCS 2007 - New York, NY, United States Duration: Jun 4 2007 → Jun 7 2007 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 4514 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | International Symposium on Logical Foundations of Computer Science, LFCS 2007 |
---|---|

Country | United States |

City | New York, NY |

Period | 6/4/07 → 6/7/07 |

### Keywords

- Convergence space
- Differential
- Discrete structure
- Hybrid structure

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Elementary differential calculus on discrete and hybrid structures'. Together they form a unique fingerprint.

## Cite this

*Logical Foundations of Computer Science - International Symposium, LFCS 2007, Proceedings*(pp. 41-53). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4514 LNCS).