Editing Spectral space (section)

==Definition==

Let ''X'' be a topological space and let ''K''<sup><math>\circ</math></sup>(''X'') be the set of all 
[[Compact space|compact]] [[Open set|open subsets]] of ''X''. Then ''X'' is said to be ''spectral'' if it satisfies all of the following conditions:
*''X'' is [[compact space|compact]] and [[Kolmogorov space|T<sub>0</sub>]].
* ''K''<sup><math>\circ</math></sup>(''X'') is a [[basis (topology)|basis]] of open subsets of ''X''.
* ''K''<sup><math>\circ</math></sup>(''X'') is [[Closure (mathematics)|closed under]] finite intersections.
* ''X'' is [[Sober space|sober]], i.e., every nonempty [[Hyperconnected space|irreducible]] [[Closed set|closed subset]] of ''X'' has a (necessarily unique) [[generic point]].