Some results related with course structure, course map and course equivalent

Abstract

Coarse space is the large scale structure of metric space similar to the tools provided by topology for analyzing behavior at small distance as topological property can be defined entirely in terms of open sets. Coarse structure depends on boundedness and degrees of freedom (dimension). A coarse map is one which preserves distance at large scale. It sends an unbounded set to an unbounded set, and does not allow finite distance to infinite upon mapping. A term which indicate that two maps are uniformly bounded and also coarse equivalent which is comprised of two coarse maps whose composition, in whichever order are close to the respective identity maps on each space. The objective of this paper is to establish some results related with coarse map, coarse equivalent.