An incomplete real tree with complete segments

Let $𝔽$ be the field of real Puiseux series and $𝒯_{𝔽}$ the $PSL (2, 𝔽)$ -homogeneous $ℚ$ -tree defined by Brumfiel. We show that completing all the segments of $𝒯_{𝔽}$ does not result in a complete metric space.

Keywords

$\Lambda$-trees, completions, non-Archimedean ordered fields

Mathematical Subject Classification

Primary: 20E08, 51M10, 54E50

Milestones

Received: 28 April 2023

Revised: 14 December 2023

Accepted: 2 March 2024

Published: 31 May 2024

Authors

Raphael Appenzeller
ETH Zürich Zürich Switzerland

Luca De Rosa
ETH Zürich Zürich Switzerland

Xenia Flamm
ETH Zürich Zürich Switzerland

Victor Jaeck
ETH Zürich Zürich Switzerland

Vol. 21, No. 1, 2024

Raphael Appenzeller, Luca De Rosa, Xenia Flamm and Victor Jaeck

Abstract

Keywords

Mathematical Subject Classification

Milestones

Authors