A simple observation about embeddings of smooth Banach spaces into C(K) spaces allows us to construct a parametrization of the separable Banach spaces using closed subsets of the interval [0,1]. The same idea is applied to the study of the isometric embedding of spaces into certain C(K) spaces with the additional condition that the functions of the image must be Lipschitz with respect to a fixed finer metric on K. The feasibility of that kind of embeddings is related to Szlenk indices.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-1-1,
author = {Mat\'\i as Raja},
title = {Two applications of smoothness in C(K) spaces},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {1-7},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-1-1}
}
Matías Raja. Two applications of smoothness in C(K) spaces. Studia Mathematica, Tome 223 (2014) pp. 1-7. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-1-1/