Ptolemy spaces with strong inversions

TL;DR

This paper proves that compact Ptolemy spaces with numerous strong inversions and containing a Ptolemy circle are Moebius equivalent to extended Euclidean spaces, revealing a deep geometric characterization.

Contribution

It establishes a new characterization of Ptolemy spaces with strong inversions as being Moebius equivalent to extended Euclidean spaces.

Findings

Ptolemy spaces with many strong inversions are Moebius equivalent to Euclidean spaces.

Presence of a Ptolemy circle is crucial for this equivalence.

The result links inversion properties to classical Euclidean geometry.

Abstract

We prove that a compact Ptolemy space with many strong inversions that contains a Ptolemy circle is Moebius equivalent to an extended Euclidean space.