Three Questions on Special Homeomorphisms on Subgroups of $R$ and $R^\infty$

TL;DR

This paper explores special homeomorphisms on subgroups of real numbers, addressing two key questions from different perspectives and discussing two variants of Anderson's Involution Conjecture.

Contribution

It offers new insights into the nature of special homeomorphisms on real subgroups and examines multiple viewpoints and conjecture variants.

Findings

Questions can be approached from different perspectives

Provides partial answers to two key questions

Discusses two versions of Anderson's Involution Conjecture

Abstract

We provide justifications for two questions on special maps on subgroups of the reals. We will show that the questions can be treated from different points of view. We also discuss two versions of Anderson's Involution Conjecture.