ANALYSIS
SEMINAR

"The
Problem of Convexity of

Chebyshev Sets"

By

Alexander Goncharov

(Bilkent University)

Abstract: A nonvoid
set $M$ of a Banach space $X$  is called a Chebyshev set if, for each $x\in X,$ its metric projection
$P_M(x)$ contains exactly one element. Every convex closed set in a strictly  convex
reflexive Banach space is Chebyshev.
The converse, the problem of convexity of Chebyshev
sets, is still open even in the case of Hilbert spaces. An introduction to the
problem is presented.

Tea and cookies will be served before the
seminar.

Date:
Tuesday, October 02, 2012

Time: 15.40

Place: Mathematics Seminar Room,
SA-141