A Few Questions on the Topologization of the Ring of Fermat Reals

TL;DR

This paper discusses the potential for developing a topological framework for the Fermat Real Line, emphasizing the opportunities for future research in this area.

Contribution

It highlights the significant open questions and the need for topological structures in the study of Fermat Reals, encouraging further exploration.

Findings

Identifies gaps in the topological understanding of Fermat Reals

Suggests the potential for rich topological structures

Encourages future research in this mathematical area

Abstract

This note is developing, and we will include many additions in the near future. Our purpose here is to highlight that there is plenty of space for a topological development of the Fermat Real Line.