Coarse amenability versus paracompactness

Recent research in coarse geometry revealed similarities between certain concepts of analysis, 
large scale geometry, and topology. Property A of G.Yu is the coarse analog of amenability for groups 
and its generalization (exact spaces) was later strengthened to be the large scale analog of paracompact 
spaces using partitions of unity. In this paper we go deeper into divulging analogies between 
coarse amenability and paracompactness. In particular, we define a new coarse analog of paracompactness 
modelled on the defining characteristics of expanders.