Space of Stone-Čech Compactification 𝜷��ℕ

Abstract

In this paper, the definition of Stone-Čech defined on the discrete topological space of the natural numbers is used, which is the set of all ultra-filters on ℕ and this is the largest compact space created from space. The algebraic and topological properties of ℕ will be used to understand and study some of the algebraic and topological properties of it. We have expanded the semi-group process (ℕ, +), naturally to the Stone-Čech compactification (𝛽ℕ, +). We use this to illustrate the structure, emphasizing on the smallest ideal 𝛽ℕ + 𝒫 where 𝒫 ∈ 𝛽ℕ. We show that 𝛽ℕ + 𝒫 containing a minimal left ideal and has the smallest ideal 𝑀(𝛽ℕ), which is also an ideal.