This is an announcement for the paper "Coarse and uniform embeddings" by Bruno de Mendonca Braga.

Abstract: In these notes, we study the relation between uniform and coarse embed= dings between Banach spaces. In order to understand this relation better, we al= so look at the problem of when a coarse embedding can be assumed to be topological. Among other results, we show that if a Banach space $X$ uniformly embeds into a minimal Banach space $Y$, then $X$ simultaneously coarsely and uniformly embeds into $Y$, and if a Banach space $X$ coarsely embeds into a minimal Banach space $Y$, then $X$ simultaneously coarsely and homeomorphically embeds into $Y$ by a map with uniformly continuous inverse.

Archive classification: math.FA

Mathematics Subject Classification: 46B80

Submitted from: demendoncabraga@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1512.03109

or

http://arXiv.org/abs/1512.03109