thin algebraic set
A subset is said to be of type if there is a closed subset , with , such that . In other words, is not dense in (with respect to the Zariski topology).
Let be a field and let be the -dimensional affine space. Then, the only Zariski-closed subsets of are finite subsets of points. Thus, the only subsets of type are subsets formed by a finite number of points.
Let be affine space and define:
by . Then . Thus, the subset:
, i.e. is the subset of perfect squares in , is a subset of type .
- 1 J.-P. Serre, Topics in Galois Theory, Research Notes in Mathematics, Jones and Barlett Publishers, London.
|Title||thin algebraic set|
|Date of creation||2013-03-22 15:14:13|
|Last modified on||2013-03-22 15:14:13|
|Last modified by||alozano (2414)|