We introduce a new approach to infinite dimensional holomorphy. Cast in the setting of closed-embedded linear convergence spaces and based on a categorical definition of derivative, our theory applies beyond the traditional open domains. It reaches certain domains with empty interior (that arise naturally in Fréchet spaces) and gives a fully fledged differential calculus. On open domains our approach provides a new characterization of holomorphic maps. Thus earlier theories become expanded as well as strengthened.

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doi.org/10.1007/BF00880045
Applied Categorical Structures
School of Mathematics and Statistics

Monadi, A., & Nel, L. (1993). Holomorphy in convergence spaces. Applied Categorical Structures, 1(2), 233–245. doi:10.1007/BF00880045