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arXiv · 1905.06521

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

G. Bezhanishvili·P. J. Morandi·B. Olberding
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Abstract

Gelfand-Naimark-Stone duality provides an algebraic counterpart of compact Hausdorff spaces in the form of uniformly complete bounded archimedean $\ell$-algebras. In [4] we extended this duality to completely regular spaces. In this article we use this extension to characterize normal, Lind\"{e}lof, and locally compact Hausdorff spaces. Our approach gives a different perspective on the classical theorems of Kat\v{e}tov-Tong and Stone-Weierstrass.

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G. Bezhanishvili, P. J. Morandi, B. Olberding. 2019-05-16. Gelfand-Naimark-Stone duality for normal spaces and insertion theorems. https://arxiv.org/abs/1905.06521

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