Applications of the Gelfand--Naimark duality
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 -algebras provides great insight into compact Hausdorff spaces, and Cech--Stone remainders and their autohomeomorphisms in particular.
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