Let a set C be given. Two subsets S,T ⊆ C are said to be orthogonal, written S ⊥ T, if S ∩ T is ∅ or a singleton. For a family of C-sets (i.e., F ⊆ ℘(C)), the dual of F, written F ⊥, is defined as the set of all C-sets S such that for every T ∈ F, S ⊥ T. A coherent space F over C is a family C-sets for which F = (F ⊥) ⊥.
In Proofs and Types coherent spaces are called coherence spaces. A footnote explains that although in the French original they were espaces cohérents, the coherence space translation was used because spectral spaces are sometimes called coherent spaces.
- Girard, J.-Y.; Lafont, Y.; Taylor, P. (1989), Proofs and types, Cambridge University Press.
- Girard, J.-Y. (2004), "Between logic and quantic: a tract", in Ehrhard; Girard; Ruet et al., Linear logic in computer science (PDF), Cambridge University Press .
- Johnstone, Peter (1982), "II.3 Coherent locales", Stone Spaces, Cambridge University Press, pp. 62–69, ISBN 978-0-521-33779-3.
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