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A differential operator and weak topology for Lipschitz maps

<13>This article, based on a LICS'08 paper, uncovers the weakest topology for the fundamental class of Lipschitz maps for which the newly constructed L-derivative operator is continuous. The L-derivative itself was discovered jointly with senior industrialist Andre Lieutier of Dassault Systems (LICS'02). The significance of this topology for Lipschitz maps is similar to that of C^1 norm topology for continuously differentiable functions, the fundamental topology used for these maps. By showing that the L-derivative operator is also computable, the article opened the way for constructing, for the first time, a PCF like functional programming language for differentiable functions in (FOSSACS'13).