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Spectral space : ウィキペディア英語版 | Spectral space In mathematics, a spectral space is a topological space that is homeomorphic to the spectrum of a commutative ring. ==Definition==
Let ''X'' be a topological space and let ''K(X)'' be the set of all quasi-compact open subsets of ''X''. Then ''X'' is said to be ''spectral'' if it satisfies all of the following conditions: *''X'' is quasi-compact and ''T0''. * ''K(X)'' is a basis of open subsets of ''X''. * ''K(X)'' is closed under finite intersections. * ''X'' is sober, i.e. every nonempty irreducible closed subset of ''X'' has a (necessarily unique) generic point.
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「Spectral space」の詳細全文を読む
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