Suppose we are given a Fréchet algebra X of functions defined on a set D. A sequence Z of distinct points \((z_k)_{k=1}^{\infty }\) in D defines an ideal J of functions equal to zero on Z. We are interested in the geometric characterization for the splitting of the short exact sequence \(0 \longrightarrow J \stackrel {i}{\longrightarrow } X \stackrel {\pi }{\longrightarrow } X/J \longrightarrow 0.\) Here the quotient space is a sequence space and the right inverse of the epimorphism (if exists) is naturally represented as an interpolating operator. We review some known cases when X is a Banach algebra of analytic functions, namely the Hardy space of bounded holomorphic functions on the unit disk and the disc algebra. Then new results are presented for the algebra of infinitely differentiable functions and Whitney algebra. Interestingly, the geometric conditions for the continuity of the corresponding interpolation projections in these cases are opposite in the following sense. For the spaces of analytic functions, arbitrary rapid convergence of \((z_k)_{k=1}^{\infty }\) to a boundary point is allowed, whereas there is an upper limit on the rate of convergence for such sequences in the second case. Also, some linear topological properties of the corresponding restriction spaces and Whitney spaces are analyzed.