The Representive of Metric Pro jection on the Finite Co dimension Subspace in Banach Space

In the paper we introduce the notions of the separation factor $κ$ and givea representive of metric projection on an $n$-codimension subspace (or an affine set)under certain conditions in Banach space. Further, we obtain the distance formulafrom any point $x$ to a finite $n$-codimension subspace. Results extend and improve thecorresponding results in Hilbert space.