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Infinite dimensional holomorphy via categorical differential calculus

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Abstract

We establish that the category of hological spaces is equipped for calculus with complex scalars. This provides a theory of infinite dimensional holomorphy which allows maps to have nonconvex domains with empty interior. Some relatively elementary functions, hitherto excluded by the restrictive definitions of other theories, emerge as holomorphic maps.

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Authors and Affiliations

  1. Yonsei University, Seoul, Korea

    K. C. Min

  2. Carleton University, Ottawa, Canada

    L. D. Nel

Authors
  1. K. C. Min
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  2. L. D. Nel
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KOSEF aided.

NSERC aided.

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Min, K.C., Nel, L.D. Infinite dimensional holomorphy via categorical differential calculus. Monatshefte für Mathematik 111, 55–68 (1991). https://doi.org/10.1007/BF01299277

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  • DOI: https://doi.org/10.1007/BF01299277

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