proof that is quasi-compact
Note that most of the notation used here is defined in the entry prime spectrum.
The following is a proof that is quasi-compact.
Let be an indexing set and be an open cover for . For every , let be an ideal of with . Since
. Thus, by this theorem (http://planetmath.org/VIemptysetImpliesIR), . Since , there exists a finite subset of such that, for every , there exists an with .
Let . Then . Thus, . Therefore, . Since
restricts to a finite subcover. It follows that is quasi-compact. ∎
|Title||proof that is quasi-compact|
|Date of creation||2013-03-22 16:07:40|
|Last modified on||2013-03-22 16:07:40|
|Last modified by||Wkbj79 (1863)|