Super differential calculus (Q1117514)

Contributing to the foundations of the theory of super manifolds, the author develops a super differential calculus on the super Euclidean space, represented as the projective limit of a system of finite dimensional Euclidean spaces [cf. \textit{I. N. Bernshtein} and \textit{B. I. Rozenfel'd}, Usp. Math. Nauk. 28, No.4, 103-138 (1973; Zbl 0285.57014)]. The underlying principle of this paper is that one can describe the concept of the super differential calculus in terms of a differential calculus on an infinite dimensional Euclidean space (op. cit.). For example, he derives the Cauchy-Riemann equations for a super smooth function more effectively than \textit{C. P. Boyer} and \textit{S. Gitler} [Trans. Am. Math. Soc. 285, 241-267 (1984; Zbl 0543.58002)] and he proves the inverse mapping theorem.