A note on inverse-closed subalgebras of C(X)
type: Item
instance of: scholarly article
title: A note on inverse-closed subalgebras of C(X)
zbMATH Open document ID: 0564.54008
DOI: 10.1007/BF01903615
published in: Acta Mathematica Hungarica
publication date: 1988-01-01T00:00:00Z
review text: The word space will refer to Tychonoff spaces. We denote C(X) for the ring of all continuous real-valued functions on a space X. By an algebra on X is meant a subring of C(X) which contains the constants, separate points and closed sets, and is closed under uniform convergence and inversion in C(X). A. W. Hager and D. G. Johnson have proved that if the Hewitt realcompactification \(\upsilon\) X is Lindelöf, then each algebra on X is isomorphic to C(Y) for some space Y and they ask whether the converse of this assertion holds. In an earlier paper [Stud. Sci. Math. Hung. (to appear); Zbl 0526.54014] the author has proved that the answer is yes if X is paracompact or X is the product \(Y\times K\), where K is a compact space of non-measurable cardinal having at least two points. In this paper we provide another partial solution to the above question by showing the equivalence when X is a Hausdorff topological group.
Mathematics Subject Classification ID: 54C40
Mathematics Subject Classification ID: 22A05
zbMATH DE Number: 3899724
zbMATH Keywords: Hausdorff topological group
zbMATH Keywords: Lindelöf Hewitt realcompactification
zbMATH Keywords: isomorphy to inverse-closed subalgebras
author: Jose L. Blasco
MaRDI profile type: Publication
cites work: Q4768316
cites work: Complete Bases and Wallman Realcompactifications
cites work: Q3270120
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cites work: Paracompactness and product spaces
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description: scientific article; zbMATH DE number 3899724