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.
Citation
Leonhard Frerick. Stanislav Shkarin. "Completeness of certain function spaces." Bull. Belg. Math. Soc. Simon Stevin 14 (3) 509 - 512, September 2007. https://doi.org/10.36045/bbms/1190994212
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