Let K be a nonempty closed convex subset of a real Banach space of dimension at least two. Suppose that K does not contain any hyperplane. Then the set of all support points of K is pathwise connected and the set Sigma(1)(K) of all norm-one support functionals of K is uncountable. This was proved for bounded K by L. Vesely and the author , and for general K by L. Vesely  using a parametric smooth variational principle. We present an alternative geometric proof of the general case in the spirit of .
|Numero di pagine||10|
|Rivista||Journal of Convex Analysis|
|Stato di pubblicazione||Pubblicato - 2013|
- Bishop-Phelps theorem
- Convex set
- support functional
- support point