Rings of continuous functions with values in a topological division ring

Vechtomov, E. M.

doi:10.1007/bf02363066

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§1 Introduction1

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Cited by 8 publications

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“…The subject of rings of continuos functions with values in a field is classic and has been studied by several authors, see for instance [1], [3], [6]. A survey article on the subject containing a great deal of results and many references is [9]. Although our characterization of path connected fields given by Theorem 4.1 is quite natural, it seems to have been missed in previous characterizations, see [6,Theorem 8].…”

Section: §1 Introductionmentioning

confidence: 99%

On a characterization of path connected topological fields

Caicedo

Mantilla-Soler

2019

Journal of Pure and Applied Algebra

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The aim of this paper is to give a characterization of path connected topological fields, inspired by the classical Gelfand correspondence between a compact Hausdorff topological space X and the space of maximal ideals of the ring of real valued continuous functions C(X, R). More explicitly, our motivation is the following question: What is the essential property of the topological field F = R that makes such a correspondence valid for all compact Hausdorff spaces? It turns out that such a perfect correspondence exists if and only if F is a path connected topological field.

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