JournalsprimsVol. 20, No. 5pp. 1091–1101

An Approach to the Dimension Theory of Continous Geometry from the Standpoint of Boolean Valued Analysis

  • Hirokazu Nishimura

    Kyoto University, Japan
An Approach to the Dimension Theory of Continous Geometry from the Standpoint of Boolean Valued Analysis cover
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Abstract

Recently Boolean valued analysis (i.e., analysis based on Boolean valued set theory) has been extensively studied by G. Takeuti [14-16]. The main purpose of this paper is to show, by using this technique, that any continuous geometry can be viewed as an irreducible continuous geometry in its center valued set theory. This makes the transition from irreducible continuous geometries to reducible ones automatic.

Cite this article

Hirokazu Nishimura, An Approach to the Dimension Theory of Continous Geometry from the Standpoint of Boolean Valued Analysis. Publ. Res. Inst. Math. Sci. 20 (1984), no. 5, pp. 1091–1101

DOI 10.2977/PRIMS/1195180884