The Snake Theorem for Unisolvent Families Original Research Article

The oscillation theorem of Karlin (the snake theorem) has been extended in a number of ways by Pinkus and others. We show that the theorem is valid for (almost) arbitrary unisolvent families where there are no continuity requirements on the upper and lower bounding functions. Under an essential additional hypothesis, the theorem is also true for varisolvent families. A number of applications to uniform approximation from unisolvent families and Chebyshev spaces are considered.