- Spectral space
In
mathematics , atopological space "X" withtopology Ω is said to be spectral if
*1) "X" iscompact and T0;
*2) The set "C(X)" of all compact-opensubset s of "(X,Ω)" is a sublattice of Ω and a base for the topology. Note that "compact-open" does not mean a set that is bothcompact andopen : such a set would be unusual in most interesting spaces. Here, it meanslocally compact . That is, a compact-open set is anopen set whose closure iscompact , where the closure of a set A is the intersection of all the closed sets that contain A;
*3) "X" is sober, that is any nonemptyclosed set "F" which is not a closure of a singleton {x} is a union of twoclosed sets which differ from "F".External links
* [http://folli.loria.fr/cds/1999/library/pdf/bezhan.pdf see 8.3 - Definition 6 and bibliography]
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