Definition
Let X be a topological space and let K(X) be the set of all quasi-compact and 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.
Read more about this topic: Spectral Space
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