Stone’s Real Gelfand Duality in Pointfree Topology
The familiar 1940 result of M. H. Stone characterizing the rings of real-valued continuous functions on compact Hausdorff spaces as certain partially ordered rings is obtained here in its pointfree form, replacing the spaces in question by appropriate frames, which avoids the classical recourse to the choice-dependent existence of maximal ideals. The main tools for this are a direct proof that the partially ordered rings involved are f-rings, the pointfree notion of rings of real-valued continuous functions, and the representation of archimedean bounded f-rings as rings of that kind.
KeywordsPrime Ideal Maximal Ideal Ring Homomorphism Compact Hausdorff Space Regular Frame
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