Gelfand-Naimark-Stone duality for normal spaces and insertion theorems

2019/05/16 by Guram Bezhanishvili, Bezhanishvili, G., Patrick J. Morandi +3
Mathematics · #06F25 #13J25 #54C30 #54D15 #54D20 #54D45 #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1905.06521

openalex publication_date 2019/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Gelfand-Naimark-Stone duality provides an algebraic counterpart of compact Hausdorff spaces in the form of uniformly complete bounded archimedean ℓ-algebras. In [4] we extended this duality to completely regular spaces. In this article we use this extension to characterize normal, Lindëlof, and locally compact Hausdorff spaces. Our approach gives a different perspective on the classical theorems of Katětov-Tong and Stone-Weierstrass.

Citations

• On Real-Valued Functions in Topological Spaces

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