Algebra in the superextensions of groups: minimal left ideals

TL;DR

This paper proves that minimal left ideals in the superextension of the integers are metrizable and topologically equivalent to those in the superextension of the 2-adic integers, revealing a deep structural similarity.

Contribution

It establishes the topological isomorphism between minimal left ideals of superextensions of Z and Z_2, highlighting a new structural connection in algebraic topology.

Findings

Minimal left ideals of λ(Z) are metrizable topological semigroups.

These ideals are topologically isomorphic to those of λ(Z_2).

The result links algebraic structures of integers and 2-adic numbers.

Abstract

We prove that the minimal left ideals of the superextension $\lambda(Z)$ of the discrete group $Z$ of integers are metrizable topological semigroups, topologically isomorphic to minimal left ideals of the superextension $\lambda(Z_2)$ of the compact group $Z_2$ of integer 2-adic numbers.