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An incomplete real tree with complete segments

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

Vol. 21 (2024), No. 1, 35–44
DOI: 10.2140/iig.2024.21.35
Abstract

Let 𝔽 be the field of real Puiseux series and 𝒯𝔽 the PSL (2, 𝔽)-homogeneous -tree defined by Brumfiel. We show that completing all the segments of 𝒯𝔽 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