Let X be a topological vector space, Y = R-n, n is an element of N, A
be a continuous linear map from X to Y. C subset of X, B be a convex s
et dense in C, and d is an element of Y be a data point. We derive con
ditions which guarantee that the set B boolean AND A(-1)(d) is nonempt
y and dense in C boolean AND A(-1)(d). Some applications to shape pres
erving interpolation and approximation are described. (C) 1998 Academi
c Press.