===Abstract Stone Duality ===
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[Abstract Stone Duality] is a revolutionary theory of topological spaces and continuous functions that treats them directly, just as traditional geometry was about lines and circles, without smashing the continuum into dust. ASD provides a natural language for real analysis that describes the solution-space of an equation continuously in its parameters, even across singularities. Since it is presented syntactically, in a way that generalises ordinary algebraic notation, it is inherently computable.

It was inpired by Marshall Stone's study of the categorical duality between topology and algebra, taking his slogan "always topologize" seriously by topologising the topology. It also exploits the analogy between continuous and computable functions, on which Dana Scott built the theory of denotational semantics of programming languages.
</blockquote>

--http://www.monad.me.uk/ASD/