Representing the Smallest Ideal and it's closure in the semigroup (βN,.) as equivalence classes under the extension of divisibility relations

2018/09/19 by Khalifa, Salahddeen
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1809.07395

Abstract

In this paper we will prove that all the elements in the smallest ideal K(βN) in the semigroup of the Stone Cech compactification (βN,.) of the discrete semigroup of natural numbers N under multiplication constitute a single equivalence class under the mid extension divisibility relation. And all the elements in the closure of the smallest ideal Cl(βN) constitute a single equivalence class under the tilde extension divisibility relation.

Related

• Levels of Ultrafilters with Extension Divisibilities
• Ideals in P _G and βG
• Divisibility in the Stone-Čech compactification
• Semigroup compactifications in terms of filters
• Ultrafilters maximal for finite embeddability