ON ALMOST INTERPOLATION

We obtain some characterizations of almost interpolation configuration s of points with respect to finite-dimensional functional spaces. Part icularly, a Schoenberg-Whitney ape characterization which is valid for any multivariate spline space relative ta an arbitrary partition of a domain A subset of R-m is presented. As a closely related problem we investigate sectional structure of finite-dimensional spaces of real f unctions on a topological space A. It is shown that under some reasona ble restrictions an A any space of this sort may be considered as piec ewise almost Chebyshev. (C) 1997 Academic Press.