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. 43-60

Title	spectral space
Canonical name	SpectralSpace
Date of creation	2013-03-22 16:22:32
Last modified on	2013-03-22 16:22:32
Owner	jocaps (12118)
Last modified by	jocaps (12118)
Numerical id	9
Author	jocaps (12118)
Entry type	Definition
Classification	msc 54A05