ABSTRACT. A study is made of those n-dimensional subspaces G of C_{0}(T) which are “weakly interpolating”. They are more general than the classical Haar or Chebyshev subspaces, or the weak Chebyshev subspaces considered in [2]. Weakly interpolating subspaces G have the property that for each f ∈ C_{0}(T) that has a unique best approximation g_{0} ∈ G, the error f − g_{0} has at least n + 1 peak points. In many cases of interest (e.g., any Chebyshev subspace or the splines), the converse is also valid.