Abstract
It is shown that isometries between the unit spheres of finite dimensional Banach spaces necessarily map antipodal points to antipodal points.
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Tingley, D. Isometries of the unit sphere. Geom Dedicata 22, 371–378 (1987). https://doi.org/10.1007/BF00147942
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DOI: https://doi.org/10.1007/BF00147942