Year: 2026
Type: preprint
Abstract: We construct real Banach spaces X and Y and a bijection U: X → Y which preserves all pairwise distances on every closed ball of radius 1/4 but is not a global isometry. The proof starts from an explicit injective map that preserves every distance at most 1/2 and shortens one longer distance. We then enlarge the source and target through a transfinite recursion that inserts every missing target point while preserving both injectivity and this distance threshold. This preprint is a revised paper based on “AI-Assisted Research Report: A counterexample to Scottish Book Problem 155” (https://doi.org/10.5281/zenodo.22168214). The PDF is also available on the author’s website: https://yoshito-ishiki-math.github.io/preprints/scottish.pdf.
Source: arXiv (Cornell University)
Author: Ishiki, Yoshito
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208832748
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