Resumen
We provide two methods for constructing smooth bump functions and for smoothly cutting off smooth functions on fractals, one using a probabilistic approach and sub-Gaussian estimates for the heat operator, and the other using the analytic theory for p.c.f. fractals and a fixed point argument. The heat semigroup (probabilistic) method is applicable to a more general class of metric measure spaces with Laplacian, including certain infinitely ramified fractals; however the cutoff technique involves some loss in smoothness. From the analytic approach we establish a Borel theorem for p.c.f. fractals, showing that to any prescribed jet at a junction point there is a smooth function with that jet. As a consequence wo prove that on p.c.f. fractal smooth fuctions may be cut of with no loss of smoothness, and thus can smoothly decomposed subordinate to an open cover. The later results provides a replacement for classical partition of unity arguments in the p.c.f. fractal setting.