TL;DR
This paper establishes a localized version of the Mazur-Ulam theorem, which characterizes isometries in normed spaces, providing new insights into their behavior in restricted regions.
Contribution
It introduces a local variant of the Mazur-Ulam theorem, extending the classical global result to localized settings in normed spaces.
Findings
Proves a local version of the Mazur-Ulam theorem
Shows isometries are affine locally under certain conditions
Extends understanding of isometries in normed spaces
Abstract
We prove a local version of the Mazur-Ulam theorem.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Mathematics and Applications