Good quantum number

For a Gödel constructive set, see constructible universe.

In topology, a constructible set in a topological space is a finite union of locally closed sets. (A set is locally closed if it is the intersection of an open set and closed set, or equivalently, if it is open in its closure.) Constructible sets form a Boolean algebra (i.e., it is closed under finite union and complementation.) In fact, the constructible sets are precisely the Boolean algebra generated by open sets and closed sets; hence, the name "constructible". The notion appears in classical algebraic geometry.

Chevalley's theorem (EGA IV, 1.8.4.) states: Let $f:X\to Y$ be a morphism of finite presentation of schemes. Then the image of any constructible set under f is constructible. In particular, the image of a variety need not be a variety, but is (under the assumptions) always a constructible set. For example, the projection of the variety $xy=1$ (the hyperbola) onto the x-axis is the x-axis minus the origin: this is a constructible set which is neither a variety nor open or closed in the plane.

In a topological space, every constructible set contains a dense open subset of its closure.

See also

• Constructible topology
• Constructible sheaf

Notes

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References

• Allouche, Jean Paul. Note on the constructible sets of a topological space.
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
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• Borel, Armand. Linear algebraic groups.
• Grothendieck, Alexander. EGA 0 §9
• Template:EGA
• Template:EGA
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

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