ABSTRACT
Part of the main theorem in this chapter states that a standard curve ƒ in a locally convex complete HM space is of class Ckiff its interpolating polynomials at any set of k + 1 infinitely close nearstandard points are infinitely near for compact convergence, their common standard parts being k-th Taylor polynomials of ƒ; this was a conjecture of Keith Stroyan. The chapter also shows that a standard curve in a locally convex HM space is of class Ckiff its p-th (0 = p = k) difference quotients at nearstandard points are S-continuous, even when only equally spaced interpolating points are considered.
