We improve the Mazur-Ulam theorem by relaxing the surjectivity condition.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm92-1-13, author = {Tadeusz Figiel and Peter \v Semrl and Jussi V\"ais\"al\"a}, title = {Isometries of normed spaces}, journal = {Colloquium Mathematicae}, volume = {91}, year = {2002}, pages = {153-154}, zbl = {1010.46009}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm92-1-13} }
Tadeusz Figiel; Peter Šemrl; Jussi Väisälä. Isometries of normed spaces. Colloquium Mathematicae, Tome 91 (2002) pp. 153-154. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm92-1-13/