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In proof theory, a coherent space is a concept introduced in the semantic study of linear logic. 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 topology, a coherent space is another name for spectral space. A continuous map between coherent spaces is called coherent if it is spectral. 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. ==References== *. *. *. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「coherent space」の詳細全文を読む スポンサード リンク
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