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Erschienen in:
2016 | OriginalPaper | Buchkapitel
10. Enriched Dualities
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Abstract
The classical Gelfand-Naimark duality expresses dual equivalence of the category of compact spaces and the category of rings of continuous \(\mathbb{R}\)-valued mappings on these spaces. The classical Stone duality expresses dual equivalence of the category of Stone spaces (compact zero-dimensional) and the category of Boolean rings of continuous mappings on Stone spaces. In this chapter we set forth representations that are, on the one hand, reminiscent of these long known classical dualities while, on the other hand, significantly different.