Abstract
The full subcategory of proximity lattices equipped with some additional structure (a certain form of negation) is equivalent to the category of compact Hausdorff spaces. Using the Stone-Gelfand-Naimark duality, we know that the category of proximity lattices with negation is dually equivalent to the category of real C * algebras. The aim of this paper is to give a new proof for this duality, avoiding the construction of spaces. We prove that the category of C * algebras is equivalent to the category of skew frames with negation, which appears in the work of Moshier and Jung on the bitopological nature of Stone duality.
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Moshier, M.A., Petrişan, D. (2009). A Duality Theorem for Real C * Algebras. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds) Algebra and Coalgebra in Computer Science. CALCO 2009. Lecture Notes in Computer Science, vol 5728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03741-2_20
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DOI: https://doi.org/10.1007/978-3-642-03741-2_20
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