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arXiv · 2603.10957

Applications of the Gelfand--Naimark duality

Ilijas Farah
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Abstract

Stone duality is an indispensable tool for the study of compact, zero-dimensional, Hausdorff spaces. In the case of general compact Hausdorff spaces one can get quite a bit of mileage by considering the `Wallman duality' between compact spaces and lattices of closed sets. I will argue that the Gelfand--Naimark duality between compact Hausdorff spaces and unital, commutative \cstar-algebras provides great insight into compact Hausdorff spaces, and \v Cech--Stone remainders and their autohomeomorphisms in particular.

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Ilijas Farah. 2026-03-11. Applications of the Gelfand--Naimark duality. https://arxiv.org/abs/2603.10957

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