mountain pass theorem
Then there exists a sequence in such that
The name of this theorem is a consequence of a simplified visualization for the objects from theorem. If we consider the set , where and are two villages, is the set of all the routes from to , and represents the altitude of point ; then the assumption (1) is equivalent to say that the villages and are separated with a mountains chain. So, the conclusion of the theorem tell us that exists a route between the villages with a minimal altitude. With other words exists a “mountain pass” .
|Title||mountain pass theorem|
|Date of creation||2013-03-22 15:19:19|
|Last modified on||2013-03-22 15:19:19|
|Last modified by||ncrom (8997)|