Heyting valued set theory and Sato hyperfunctions
type: Item
instance of: scholarly article
title: Heyting valued set theory and Sato hyperfunctions
zbMATH Open document ID: 0614.03058
author: Hirokazu Nishimura
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1986-01-01T00:00:00Z
review text: \textit{C. Rousseau} [Lect. Notes Math. 753, 623-659 (1979; Zbl 0433.32003)] has demonstrated that standard function theory of n variables is no other than intuitionistic function theory of one variable over \(C^{n-1}\). \textit{G. Takeuti} and \textit{S. Titani} [Global intuitionistic analysis, Preprint] have pursued the same idea in the realm of complex manifolds to find out that vector bundles over a complex manifold are apartness vector spaces, that families of complex structures are simply complex manifolds, and so on. Following these lines, this paper shows that Sato hyperfunctions with holomorphic parameters can be viewed as those without parameters in an appropriately chosen intuitionistic universe, where we establish, as an application of this idea, de Rham and Dolbeault theorems with hyperfunctional coefficients.
Mathematics Subject Classification ID: 03F55
Mathematics Subject Classification ID: 32A10
Mathematics Subject Classification ID: 32Q99
zbMATH DE Number: 3993584
zbMATH Keywords: de Rham theorem
zbMATH Keywords: intuitionistic set theory
zbMATH Keywords: Dolbeault theorem
zbMATH Keywords: Sato hyperfunctions with holomorphic parameters
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195177631
OpenAlex ID: W2058295764
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DOI: 10.2977/PRIMS/1195177631
description: scientific article; zbMATH DE number 3993584