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Abstract Stone duality
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In mathematics, Abstract Stone Duality (ASD) is a paradigm for general topology which deals directly with topological spaces instead of defining them via sets. Every expression therefore automatically denotes a computable continuous function. Like locale theory, ASD was inspired by Stone duality between topology and algebra. However, whereas a locale is defined by a set with lattice structure, the carrier in ASD is another space of the kind being defined. This was originally formulated in category theory using the notion of monad, but has now been given a type-theoretic presentation. It provides a complete axiomatisation of computably based locally compact spaces. The best introduction to ASD for the general mathematician is provided by its application to the intermediate value theorem in non-classical analysis. |
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