spectral space

A topological space is called spectral if

• it is compact,

• Kolmogorov (also called $T_0$ (http://planetmath.org/T0)),

• compactness is preserved upon finite intersection of open compact sets, and

• 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.

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