Two different works in mathematical physics are presented:A construction of conformal infinity in null and spatial directions is constructedfor the Rainbow-flat space-time corresponding to doubly special relativity. Fromthis construction a definition of asymptotic DSRness is put forward which is com-patible with the correspondence principle of Rainbow gravity. Furthermore a resultequating asymptotically flat space-times with asymptotically DSR spacetimes ispresented.An overview of microlocality in braided ribbon networks is presented. Follow-ing this, a series of definitions are presented to explore the concept of microlocalityand the topology of ribbon networks. Isolated substructure of ribbon networks areintroduced, and a theorem is proven that allows them to be relocated. This is fol-lowed by a demonstration of microlocal translations. Additionally, an investigationinto macrolocality and the implications of invariants in braided ribbon networksare presented.
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