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arXiv · hep-th/9408114

Discrete Differential Manifolds and Dynamics on Networks

A. Dimakis·F. M"uller-Hoissen·F. Vanderseypen
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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.

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A. Dimakis, F. M"uller-Hoissen, F. Vanderseypen. 1994-08-21. Discrete Differential Manifolds and Dynamics on Networks. https://doi.org/10.1063/1.530996

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