M. R. Haddadi - Faculty of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
J. Hamzenejad

In this paper  we give newresults on the best approximation  in the Hausdorff topological vectorspace and  consider relationship  with orthogonality. Also we determined under  what conditions the map $P_{K,f}$ is upper semicontinous.