Completeness of certain function spaces

Frerick, Leonhard; Shkarin, Stanislav

Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, p. 509-512 / Harvested from Project Euclid

Résumé

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.

Publié le : 2007-09-14
Classification:

@article{1190994212,
     author = {Frerick, Leonhard and Shkarin, Stanislav},
     title = {Completeness of certain function spaces},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {13},
     number = {5},
     year = {2007},
     pages = { 509-512},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1190994212}
}

Frerick, Leonhard; Shkarin, Stanislav. Completeness of certain function spaces. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp.  509-512. http://gdmltest.u-ga.fr/item/1190994212/