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arXiv · 2209.01406

Decompositions in direct sum of seminormed vector spaces and Mazur-Ulam theorem

Oleksiy Dovgoshey·Jürgen Prestin·Igor Shevchuk
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Abstract

It was proved by S. Mazur and S. Ulam in 1932 that every isometric surjection between normed real vector spaces is affine. We generalize the Mazur--Ulam theorem and find necessary and sufficient conditions under which distance-preserving mappings between seminormed real vector spaces are linear.

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Oleksiy Dovgoshey, Jürgen Prestin, Igor Shevchuk. 2022-09-03. Decompositions in direct sum of seminormed vector spaces and Mazur-Ulam theorem. https://arxiv.org/abs/2209.01406

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