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On the Addition Modulus of the Aunu Pattern ω_i ϵ G_p: An Investigation of Some Topological Properties

Abstract

Suleiman I, Ibrahim AA and Ejima O

This paper investigates the topological properties on the structure generated by the addition modulus of the Aunu permutation pattern 𝑤𝑖. The pattern 𝑤𝑖 has the generating function defined as:

𝜔𝑖=(1 (1+𝑖)𝑚𝑜𝑑𝑝 (1+2𝑖)𝑚𝑜𝑑𝑝 (1+3𝑖)𝑚𝑜𝑑𝑝………(1+((𝑝−1)𝑖)𝑚𝑜𝑑𝑝)

For 𝑖=1,2,..𝑝−1.

The numbers are arrangement on the structure 𝑋={1,….,𝑃} for primes p ≥ 5.

It has been established in this paper that the generated set is a topology on 𝑋, it is not a convex set and finally, not a 𝜎-algebra.