SOBER SPACES AND CONTINUATIONS
Paul J. Taylor · 2002
A topological space is sober if it has exactly the points that are dictated by its open sets. We explain the analogy with the way in which computational values are determined by the observations that can be made of them. A new definition of sobriety is formulated in terms of lambda calculus and elementary category theory, with no reference to lattice structure, but, for topological spaces, this coincides with the standard lattice-theoretic definition. The primitive symbolic and categorical structures are extended to make their types sober. For the natural numbers, the additional structure provides definition by description and general recursion.