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Abstract
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Let
be the field of real
Puiseux series and
the
-homogeneous
-tree
defined by Brumfiel. We show that completing all the segments of
does
not result in a complete metric space.
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Keywords
$\Lambda$-trees, completions, non-Archimedean ordered
fields
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Mathematical Subject Classification
Primary: 20E08, 51M10, 54E50
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Milestones
Received: 28 April 2023
Revised: 14 December 2023
Accepted: 2 March 2024
Published: 31 May 2024
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© 2024 The Author(s), under
exclusive license to MSP (Mathematical Sciences
Publishers). |
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