| This article describes the classical Mazur-Ulam Theorem of isometry in normed spaces and its generalizations. First,a converse partial of the Baker theorem is proved.Then,in the case of non-surjection,it is proved that if the images project to the unit sphere constitute a sufficiently dense net,then the operator is linear. And the result is also hold for the maps which keep the distance equation. Finally, the Mazur-Ulam Theorem is promoted in a special metric linear space. |
