Abstract:
In this paper, partial ordered relation is researched, finite geometry and its subgeometries are explored. An investigation of topology which exists in near-linear and non-near-linear finite geometry Gd is delved into. The outcome of this work shows an existence of the concept of topology and topological space on non-near-linear finite geometry with variables in Zd. The complexity shown in this work demonstrated the existence of relationship between a geometry as a structure and its subgeometries as its substructures.
Description:
Let Z^+represents a set of positive integers. Z_d, the ring of integers modulo d, where d∈Z^+. For quite some time, finite quantum systems with variables in Z_d had received enormous attention with a special focus on mutually unbiased bases. Likewise in recent times, the weak mutually unbiased bases are getting more interest from researchers. This might be because such concepts have a significant role in quantum computation and information. For instance, discussed an existence of lattice structure between lines in near-linear finite geometries and its sublines. This paper establishes a relationship between topological space and the concept of non-near-linear finite geometry with variables in Z_d.
