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Gelfand-Naimark-Stone duality provides an algebraic counterpart of compactHausdorff 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, andlocally compact Hausdorff spaces. Our approach gives a different perspective onthe classical theorems of Kat\v{e}tov-Tong and Stone-Weierstrass.

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