Heyting valued set theory and fibre bundles
type: Item
instance of: scholarly article
title: Heyting valued set theory and fibre bundles
zbMATH Open document ID: 0654.03046
author: Hirokazu Nishimura
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1988-01-01T00:00:00Z
review text: \textit{G. Takeuti} and \textit{S. Titani} [Ann. Pure Appl. Logic 31, 307-339 (1986; Zbl 0615.03048)] have demonstrated that, given a manifold B with topology \(\Omega ={\mathcal O}(B)\), the internal notion of an apartness vector space in \(v^{(\Omega)}\) and the external notion of a vector bundle over B are no more than two representations of the same entity. The principal objective of this paper is, first of all, to internalize fibre bundles on the lines of their paper, and then to establish various internal-external interconnections. For example, we show that the external notion of integration over a fibre corresponds to the usual integration on internalized manifolds within \(V^{(\Omega)}\). The paper attains its climax as we discuss the internal and external aspects of an internalized version of celebrated Stokes' theorem.
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 03F55
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 55R10
Mathematics Subject Classification ID: 03E40
zbMATH DE Number: 4066878
zbMATH Keywords: Heyting valued set theory
zbMATH Keywords: fibre bundles
zbMATH Keywords: internal-external interconnections
zbMATH Keywords: integration on internalized manifolds
zbMATH Keywords: Stokes' theorem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195175197
OpenAlex ID: W1980048809
DOI: 10.2977/PRIMS/1195175197
description: scientific article; zbMATH DE number 4066878