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.

Additional Metadata
Keywords analyte, categorical differentiation theory, categorical methods, closed-embedded linear convergence spaces, Infinite dimensional holomorphy, Mathematics Subject Classifications (1991): Primary: 46G20, Secondary: 58B12, 46M40
Persistent URL dx.doi.org/10.1007/BF00880045
Journal Applied Categorical Structures
Monadi, A., & Nel, L. (1993). Holomorphy in convergence spaces. Applied Categorical Structures, 1(2), 233–245. doi:10.1007/BF00880045