In reflexive Banach spaces with some degree of uniform convexity, we obtain estimates for Kottman's separation constant in terms of the corresponding modulus.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-1-7, author = {Elisabetta Maluta and Pier Luigi Papini}, title = {Estimates for Kottman's separation constant in reflexive Banach spaces}, journal = {Colloquium Mathematicae}, volume = {116}, year = {2009}, pages = {105-119}, zbl = {1183.46016}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-1-7} }
Elisabetta Maluta; Pier Luigi Papini. Estimates for Kottman's separation constant in reflexive Banach spaces. Colloquium Mathematicae, Tome 116 (2009) pp. 105-119. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-1-7/