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Starting from the Colombeau's full generalized functions, the sharptopologies and the notion of generalized points, we introduce a new kinddifferential calculus (for functions between totally disconnected spaces). Westudy generalized pointvalues, Colombeau's differential algebra, holomorphicand analytic functions. We show that the Embedding Theorem and the Open MappingTheorem hold in this framework. Moreover, we study some applications indifferential equations.

A Discontinuous Differential Calculus in the Framework Colombeau's Full Algebra