Proximinal Subspaces of C(Q) of Finite Codimension Original Research Article

In this paper we investigate the structure of a proximinal subspace G of C(Q) of codimension n, in terms of the geometry of the range of the vector measure ν=(ν1, …, νn), where {ν1, …, νn} is a basis for the annihilator G⊥. In particular, we prove that if ν is non-atomic, G is proximinal iff for every P∈Ext R(ν) there exists a clopen subset C of ∪ni=1 S(νi) such that ν(C)=P.