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. The dual of a family F ⊆ ℘(C) is the family F ⊥ of all subsets S ⊆ C orthogonal to every member of F, i.e., such that S ⊥ T for all T ∈ F. 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 (PDF), Cambridge University Press.
- Girard, J.-Y. (2004), "Between logic and quantic: a tract", in Ehrhard; Girard; Ruet; et al., Linear logic in computer science, 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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