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Discrete Differential Manifolds and Dynamics on Networks | | A. Dimakis
; F. M"uller-Hoissen
; F. Vanderseypen
; | | Date: |
21 Aug 1994 | | Journal: | J.Math.Phys. 36 (1995) 3771-3791 | | Abstract: | A `discrete differential manifold’ we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with a convenient framework for the formulation of dynamical models on networks and physical theories with discrete space and time. We present several examples and introduce a notion of differentiability of maps between discrete differential manifolds. Particular attention is given to differentiable curves in such spaces. Every discrete differentiable manifold carries a topology and we show that differentiability of a map implies continuity. | | Source: | arXiv, hep-th/9408114 | | Services: | Forum | Review | PDF | Favorites | |
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