Large scale versus small scale

Recent research in coarse geometry revealed similarities between certain concepts of large scale geometry 
and topology. It is less known that a small scale analog of topology has been developed much earlier 
in the form of the uniform category.

This paper is devoted to an exposition of analogies between basic concepts of topology (paracompactness, 
covering dimension), important ideas of coarse geometry (Property A of G. Yu, asymptotic dimension of 
M. Gromov), and notions from the uniform category (l_1-property, the uniform dimension).