Abstract Stone duality

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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