A Note on the Proof of Theorem 13 in the Paper "Generalized Gyrovector Spaces and a Mazur-Ulam theorem"

TL;DR

This paper revises the proof of a Mazur-Ulam theorem within generalized gyrovector spaces, clarifying and correcting the original proof to strengthen the theoretical foundation of the subject.

Contribution

It provides a corrected and clearer proof of the Mazur-Ulam theorem for generalized gyrovector spaces, enhancing the mathematical rigor of the original work.

Findings

Revised proof of the Mazur-Ulam theorem for generalized gyrovector spaces

Clarification of key steps in the original proof

Strengthened theoretical understanding of gyrovector space isometries

Abstract

We give a revision of the proof of a Mazur-Ulam theorem for generalized gyrovector spaces given in the paper "Generalized gyrovector spaces and a Mazur-Ulam theorem" published in Publ. Math. Debrecen, 87 (2015), 393--413.