**"****Existence and Uniqueness of Best Approximations **

**in Metric Spaces****"**

By

__Senior Project Presentation__

**Abstract:** In a metric space X a best
approximation of a given point P to a set M is the
point Q in M that is nearest to P. But such a point may or may
not exist and there may be several of them. We discuss existence and uniqueness of
best approximations. Also we give some information about problem of convexity
of

Chebyshev sets.

**Date: ****Tuesday, May 13, 2013**

**Time: ****15.40**

**Place: ****Mathematics Seminar Room,
SA-141**

Tea and cookies will be served before the
seminar.