Abstract & Overview
Two different works in mathematical physics are presented: \n A construction of conformal infinity in null and spatial directions is constructed \nfor the Rainbow-flat space-time corresponding to doubly special relativity. From \nthis construction a definition of asymptotic DSRness is put forward which is com- \npatible with the correspondence principle of Rainbow gravity. Furthermore a result \nequating asymptotically flat space-times with asymptotically DSR spacetimes is \npresented. \n An overview of microlocality in braided ribbon networks is presented. Follow- \ning this, a series of definitions are presented to explore the concept of microlocality \nand the topology of ribbon networks. Isolated substructure of ribbon networks are \nintroduced, and a theorem is proven that allows them to be relocated. This is fol- \nlowed by a demonstration of microlocal translations. Additionally, an investigation \ninto macrolocality and the implications of invariants in braided ribbon networks \nare presented.