In Abstract Stone Duality the topology on a space X is treated, not as an infinitary lattice, but... more In Abstract Stone Duality the topology on a space X is treated, not as an infinitary lattice, but as an exponential space Σ X . This has an associated lambda calculus, in which monadicity of the self-adjunction Σ − Σ − makes all spaces sober and gives subspaces the subspace topology, and the Euclidean principle F σ ∧ σ = F ∧ σ makes Σ the classifier for open subspaces. Computably based locally compact locales provide the leading model for these axioms, although the methods are also applicable to CCD op (constructively completely distributive lattices).
In Abstract Stone Duality the topology on a space X is treated, not as an infinitary lattice, but... more In Abstract Stone Duality the topology on a space X is treated, not as an infinitary lattice, but as an exponential space Σ X . This has an associated lambda calculus, in which monadicity of the self-adjunction Σ − Σ − makes all spaces sober and gives subspaces the subspace topology, and the Euclidean principle F σ ∧ σ = F ∧ σ makes Σ the classifier for open subspaces. Computably based locally compact locales provide the leading model for these axioms, although the methods are also applicable to CCD op (constructively completely distributive lattices).
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