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/