@inproceedings{a7b7100dc6034536b247d105a1c184f9,

title = "Elementary differential calculus on discrete and hybrid structures",

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.",

keywords = "Convergence space, Differential, Discrete structure, Hybrid structure",

author = "Blair, {Howard A.} and Jakel, {David W.} and Irwin, {Robert J.} and Angel Rivera",

year = "2007",

doi = "10.1007/978-3-540-72734-7_4",

language = "English (US)",

isbn = "3540727329",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "41--53",

booktitle = "Logical Foundations of Computer Science - International Symposium, LFCS 2007, Proceedings",

note = "International Symposium on Logical Foundations of Computer Science, LFCS 2007 ; Conference date: 04-06-2007 Through 07-06-2007",

}