Applied Categorical Structures

, Volume 1, Issue 2, pp 233–245 | Cite as

Holomorphy in convergence spaces

  • A. Monadi
  • L. D. Nel
Article

Abstract

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.

Mathematics Subject Classifications (1991)

Primary: 46G20 Secondary: 58B12, 46M40 

Key words

Infinite dimensional holomorphy closed-embedded linear convergence spaces analyte categorical methods categorical differentiation theory 

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • A. Monadi
    • 1
  • L. D. Nel
    • 1
  1. 1.Department of Mathematics and StatisticsCarleton UniversityOttawaCanada

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