spectral space
A topological space^{} is called spectral if

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it is compact^{},

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Kolmogorov (also called ${T}_{0}$ (http://planetmath.org/T0)),

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compactness is preserved upon finite intersection^{} of open compact sets, and

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any nonempty irreducible^{} subspace^{} of it contains a generic point
In his thesis, Mel Hochster showed that for any spectral space there is commutative^{} unitary ring whose prime spectrum is homeomorphic to the spectral space.
References
 1 M. Hochster, ”Prime Ideal^{} Structure^{} in Commutative Rings”, Transactions of American Mathematical Society, Aug. 1969, vol. 142, p. 4360
Title  spectral space 

Canonical name  SpectralSpace 
Date of creation  20130322 16:22:32 
Last modified on  20130322 16:22:32 
Owner  jocaps (12118) 
Last modified by  jocaps (12118) 
Numerical id  9 
Author  jocaps (12118) 
Entry type  Definition 
Classification  msc 54A05 