Completeness of certain function spaces

Abstract

We give an example of a complete locally convex m-topology on the algebra of infinite differentiable functions on $[0,1]$ which is strictly coarser than the natural Fréchet-topology but finer than the topology of pointwise convergence. A similar construction works on the algebra of continuous functions on $[0,1].$ Using this examples we can separate different notions of diffotopy and homotopy.